4-ary Boolean functions

Studies of Boolean functions

Venn diagram of the Boolean function
0000 0001 0001 0110

There are  2 2 4 {\displaystyle 2^{2^{4}}} = 65536 4-ary Boolean functions, which correspond to 16-bit binary strings.

## Big equivalence classes (bec)

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Compare: Big equivalence classes of 3-ary Boolean functions

When binarily colored tesseracts can be transformed into each other by actions in the tesseract's symmetry group C4, they are essentially the same.
The corresponding Boolean functions are often called equivalent and belong to the same big equivalence class (bec).
The 65536 functions belong to 1 + 1 + 4 + 6 + 19 + 27 + 50 + 56 + 74 + 56 + 50 + 27 + 19 + 6 + 4 + 1 + 1 = 402 becs.

The following sortable table (in the collapsed box) shows the 402 becs with some key features.
The default order is that of the numbers in column N. Sorting by # sorts also by N.
The numbers in column weight are the hamming weights of the functions, i.e. the number of ones in the binary strings.
Column sec tells the number of secs in the bec. Column f tells the number of functions in the bec.
The function with the smallest numerical value is shown in column F as an example. It's numerical value is shown in column N.
becs with an entry in column sona are related to subgroups of nimber addition.
The entry in column wec denotes the Walsh equivalence class the bec belongs to.
The nonlinearity of all functions in the bec is shown in column nonlin.
Functions with nonlinearity 0 are linear, those with nonlinearity 6 are bent.
To sort by more than one column you can hold the shift-key and than click the other sort buttons. *

Table of the 402 becs

The binary strings are interpreted as reverse binary numbers. | #  | weight  | sec  | f  | F  | N  | sona  | wec  | nonlin

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0 |  0 | 1 | 1 | .... .... .... .... | 0 |  | E0 | 0
1 |  1 | 1 | 16 | !... .... .... .... | 1 | N(0) | O | 1
2 |  2 | 4 | 32 | !!.. .... .... .... | 3 | N(1,1) | E1 | 2
3 |  2 | 6 | 48 | .!!. .... .... .... | 6 | N(1,2) | E2 | 2
4 |  3 | 6 | 96 | !!!. .... .... .... | 7 |  | O | 3
5 |  4 | 6 | 24 | !!!! .... .... .... | 15 | N(2,1) | E0 | 4
6 |  3 | 4 | 64 | .!!. !... .... .... | 22 |  | O | 3
7 |  4 | 4 | 64 | !!!. !... .... .... | 23 |  | E3 | 4
8 |  2 | 4 | 32 | ...! !... .... .... | 24 | N(1,3) | E3 | 2
9 |  3 | 12 | 192 | !..! !... .... .... | 25 |  | O | 3
10 |  4 | 12 | 192 | !!.! !... .... .... | 27 |  | E2 | 4
11 |  4 | 12 | 192 | .!!! !... .... .... | 30 |  | E1 | 4
12 |  5 | 12 | 192 | !!!! !... .... .... | 31 |  | O | 3
13 |  4 | 12 | 48 | ..!! !!.. .... .... | 60 | N(2,2) | E0 | 4
14 |  5 | 12 | 192 | !.!! !!.. .... .... | 61 |  | O | 3
15 |  6 | 12 | 96 | !!!! !!.. .... .... | 63 |  | E1 | 2
16 |  4 | 4 | 16 | !..! .!!. .... .... | 105 | N(2,3) | E0 | 4
17 |  5 | 4 | 64 | !!.! .!!. .... .... | 107 |  | O | 3
18 |  6 | 12 | 96 | !!!! .!!. .... .... | 111 |  | E2 | 2
19 |  6 | 4 | 32 | .!!! !!!. .... .... | 126 |  | E3 | 2
20 |  7 | 4 | 64 | !!!! !!!. .... .... | 127 |  | O | 1
21 |  8 | 4 | 8 | !!!! !!!! .... .... | 255 | N(3,1) | E0 | 0
22 |  4 | 1 | 16 | .!!. !... !... .... | 278 |  | E4 | 4
23 |  5 | 1 | 16 | !!!. !... !... .... | 279 |  | O | 5
24 |  3 | 6 | 96 | ...! !... !... .... | 280 |  | O | 3
25 |  4 | 6 | 96 | !..! !... !... .... | 281 |  | E4 | 4
26 |  4 | 12 | 192 | .!.! !... !... .... | 282 |  | E3 | 4
27 |  5 | 12 | 192 | !!.! !... !... .... | 283 |  | O | 5
28 |  5 | 6 | 96 | .!!! !... !... .... | 286 |  | O | 5
29 |  6 | 6 | 96 | !!!! !... !... .... | 287 |  | E2 | 4
30 |  4 | 12 | 192 | ..!! .!.. !... .... | 300 |  | E2 | 4
31 |  5 | 24 | 384 | !.!! .!.. !... .... | 301 |  | O | 5
32 |  6 | 12 | 192 | !!!! .!.. !... .... | 303 |  | E3 | 4
33 |  5 | 12 | 192 | ..!! !!.. !... .... | 316 |  | O | 3
34 |  6 | 12 | 192 | !.!! !!.. !... .... | 317 |  | E1 | 4
35 |  6 | 12 | 192 | .!!! !!.. !... .... | 318 |  | E2 | 4
36 |  7 | 12 | 192 | !!!! !!.. !... .... | 319 |  | O | 3
37 |  4 | 4 | 64 | ...! .!!. !... .... | 360 |  | E1 | 4
38 |  5 | 4 | 64 | !..! .!!. !... .... | 361 |  | O | 3
39 |  5 | 12 | 192 | .!.! .!!. !... .... | 362 |  | O | 5
40 |  6 | 12 | 192 | !!.! .!!. !... .... | 363 |  | E2 | 4
41 |  6 | 12 | 192 | .!!! .!!. !... .... | 366 |  | E3 | 4
42 |  7 | 12 | 192 | !!!! .!!. !... .... | 367 |  | O | 3
43 |  7 | 4 | 64 | .!!! !!!. !... .... | 382 |  | O | 3
44 |  8 | 4 | 64 | !!!! !!!. !... .... | 383 |  | E4 | 2
45 |  2 | 1 | 8 | .... ...! !... .... | 384 | N(1,4) | E4 | 2
46 |  3 | 4 | 64 | !... ...! !... .... | 385 |  | O | 3
47 |  3 | 3 | 48 | .!.. ...! !... .... | 386 |  | O | 3
48 |  4 | 12 | 192 | !!.. ...! !... .... | 387 |  | E3 | 4
49 |  4 | 6 | 96 | .!!. ...! !... .... | 390 |  | E2 | 4
50 |  5 | 12 | 192 | !!!. ...! !... .... | 391 |  | O | 5
51 |  4 | 6 | 96 | !..! ...! !... .... | 393 |  | E2 | 4
52 |  5 | 12 | 192 | !!.! ...! !... .... | 395 |  | O | 5
53 |  6 | 6 | 96 | !!!! ...! !... .... | 399 |  | E4 | 4
54 |  5 | 4 | 64 | .!!. !..! !... .... | 406 |  | O | 3
55 |  6 | 4 | 64 | !!!. !..! !... .... | 407 |  | E1 | 4
56 |  4 | 12 | 192 | ...! !..! !... .... | 408 |  | E1 | 4
57 |  5 | 12 | 192 | !..! !..! !... .... | 409 |  | O | 3
58 |  5 | 24 | 384 | .!.! !..! !... .... | 410 |  | O | 5
59 |  6 | 24 | 384 | !!.! !..! !... .... | 411 |  | E2 | 4
60 |  6 | 12 | 192 | .!!! !..! !... .... | 414 |  | E3 | 4
61 |  7 | 12 | 192 | !!!! !..! !... .... | 415 |  | O | 3
62 |  4 | 6 | 96 | ...! .!.! !... .... | 424 |  | E2 | 4
63 |  5 | 12 | 192 | !..! .!.! !... .... | 425 |  | O | 5
64 |  5 | 6 | 96 | .!.! .!.! !... .... | 426 |  | O | 3
65 |  6 | 12 | 192 | !!.! .!.! !... .... | 427 |  | E1 | 4
66 |  5 | 24 | 384 | ..!! .!.! !... .... | 428 |  | O | 5
67 |  6 | 24 | 384 | !.!! .!.! !... .... | 429 |  | E3 | 4
68 |  6 | 24 | 384 | .!!! .!.! !... .... | 430 |  | E2 | 4
69 |  7 | 24 | 384 | !!!! .!.! !... .... | 431 |  | O | 3
70 |  6 | 12 | 192 | ..!! !!.! !... .... | 444 |  | E4 | 4
71 |  7 | 12 | 192 | !.!! !!.! !... .... | 445 |  | O | 3
72 |  7 | 12 | 192 | .!!! !!.! !... .... | 446 |  | O | 3
73 |  8 | 12 | 192 | !!!! !!.! !... .... | 447 |  | E3 | 2
74 |  5 | 4 | 64 | ...! .!!! !... .... | 488 |  | O | 5
75 |  6 | 4 | 64 | !..! .!!! !... .... | 489 |  | E4 | 4
76 |  6 | 12 | 192 | .!.! .!!! !... .... | 490 |  | E3 | 4
77 |  7 | 12 | 192 | !!.! .!!! !... .... | 491 |  | O | 3
78 |  7 | 12 | 192 | .!!! .!!! !... .... | 494 |  | O | 3
79 |  8 | 12 | 192 | !!!! .!!! !... .... | 495 |  | E2 | 2
80 |  8 | 4 | 64 | .!!! !!!! !... .... | 510 |  | E1 | 2
81 |  9 | 4 | 64 | !!!! !!!! !... .... | 511 |  | O | 1
82 |  6 | 4 | 32 | ..!! !!.. !!.. .... | 828 |  | E1 | 2
83 |  7 | 4 | 64 | !.!! !!.. !!.. .... | 829 |  | O | 3
84 |  8 | 4 | 32 | !!!! !!.. !!.. .... | 831 |  | E0 | 4
85 |  6 | 3 | 48 | .!!. !.!. !!.. .... | 854 |  | E0 | 6
86 |  7 | 3 | 48 | !!!. !.!. !!.. .... | 855 |  | O | 5
87 |  5 | 12 | 192 | ...! !.!. !!.. .... | 856 |  | O | 5
88 |  6 | 12 | 192 | !..! !.!. !!.. .... | 857 |  | E0 | 6
89 |  6 | 24 | 384 | .!.! !.!. !!.. .... | 858 |  | E1 | 4
90 |  7 | 24 | 384 | !!.! !.!. !!.. .... | 859 |  | O | 5
91 |  7 | 12 | 192 | .!!! !.!. !!.. .... | 862 |  | O | 5
92 |  8 | 12 | 192 | !!!! !.!. !!.. .... | 863 |  | E2 | 4
93 |  5 | 12 | 192 | ...! .!!. !!.. .... | 872 |  | O | 5
94 |  6 | 12 | 192 | !..! .!!. !!.. .... | 873 |  | E1 | 4
95 |  6 | 12 | 192 | .!.! .!!. !!.. .... | 874 |  | E0 | 6
96 |  7 | 12 | 192 | !!.! .!!. !!.. .... | 875 |  | O | 5
97 |  6 | 24 | 384 | ..!! .!!. !!.. .... | 876 |  | E2 | 4
98 |  7 | 24 | 384 | !.!! .!!. !!.. .... | 877 |  | O | 5
99 |  7 | 24 | 384 | .!!! .!!. !!.. .... | 878 |  | O | 5
100 |  8 | 24 | 384 | !!!! .!!. !!.. .... | 879 |  | E1 | 4
101 |  7 | 12 | 192 | ..!! !!!. !!.. .... | 892 |  | O | 3
102 |  8 | 12 | 192 | !.!! !!!. !!.. .... | 893 |  | E3 | 4
103 |  8 | 12 | 192 | .!!! !!!. !!.. .... | 894 |  | E2 | 4
104 |  9 | 12 | 192 | !!!! !!!. !!.. .... | 895 |  | O | 3
105 |  4 | 4 | 16 | .... ..!! !!.. .... | 960 | N(2,4) | E0 | 4
106 |  5 | 12 | 192 | !... ..!! !!.. .... | 961 |  | O | 3
107 |  6 | 12 | 96 | !!.. ..!! !!.. .... | 963 |  | E1 | 2
108 |  6 | 12 | 192 | !.!. ..!! !!.. .... | 965 |  | E1 | 4
109 |  6 | 12 | 192 | .!!. ..!! !!.. .... | 966 |  | E2 | 4
110 |  7 | 24 | 384 | !!!. ..!! !!.. .... | 967 |  | O | 3
111 |  8 | 12 | 96 | !!!! ..!! !!.. .... | 975 |  | E0 | 4
112 |  6 | 12 | 192 | ..!. !.!! !!.. .... | 980 |  | E2 | 4
113 |  7 | 12 | 192 | !.!. !.!! !!.. .... | 981 |  | O | 5
114 |  7 | 12 | 192 | .!!. !.!! !!.. .... | 982 |  | O | 5
115 |  8 | 12 | 192 | !!!. !.!! !!.. .... | 983 |  | E3 | 4
116 |  6 | 12 | 192 | ...! !.!! !!.. .... | 984 |  | E3 | 4
117 |  7 | 24 | 384 | !..! !.!! !!.. .... | 985 |  | O | 5
118 |  8 | 12 | 192 | !!.! !.!! !!.. .... | 987 |  | E2 | 4
119 |  7 | 24 | 384 | ..!! !.!! !!.. .... | 988 |  | O | 3
120 |  8 | 24 | 384 | !.!! !.!! !!.. .... | 989 |  | E2 | 4
121 |  8 | 24 | 384 | .!!! !.!! !!.. .... | 990 |  | E1 | 4
122 |  9 | 24 | 384 | !!!! !.!! !!.. .... | 991 |  | O | 3
123 |  8 | 12 | 96 | ..!! !!!! !!.. .... | 1020 |  | E0 | 4
124 |  9 | 12 | 192 | !.!! !!!! !!.. .... | 1021 |  | O | 3
125 | 10 | 12 | 96 | !!!! !!!! !!.. .... | 1023 |  | E1 | 2
126 |  4 | 3 | 12 | .... .!!. .!!. .... | 1632 | N(2,5) | E0 | 4
127 |  5 | 3 | 48 | !... .!!. .!!. .... | 1633 |  | O | 3
128 |  5 | 6 | 96 | .!.. .!!. .!!. .... | 1634 |  | O | 3
129 |  6 | 12 | 192 | !!.. .!!. .!!. .... | 1635 |  | E1 | 4
130 |  6 | 6 | 48 | .!!. .!!. .!!. .... | 1638 |  | E2 | 2
131 |  7 | 6 | 96 | !!!. .!!. .!!. .... | 1639 |  | O | 3
132 |  6 | 6 | 48 | !..! .!!. .!!. .... | 1641 |  | E2 | 2
133 |  7 | 6 | 96 | !!.! .!!. .!!. .... | 1643 |  | O | 3
134 |  8 | 6 | 48 | !!!! .!!. .!!. .... | 1647 |  | E0 | 4
135 |  6 | 12 | 192 | .!.. !!!. .!!. .... | 1650 |  | E2 | 4
136 |  7 | 12 | 192 | !!.. !!!. .!!. .... | 1651 |  | O | 5
137 |  7 | 12 | 192 | .!!. !!!. .!!. .... | 1654 |  | O | 3
138 |  8 | 12 | 192 | !!!. !!!. .!!. .... | 1655 |  | E3 | 4
139 |  6 | 12 | 192 | ...! !!!. .!!. .... | 1656 |  | E3 | 4
140 |  7 | 12 | 192 | !..! !!!. .!!. .... | 1657 |  | O | 3
141 |  7 | 24 | 384 | .!.! !!!. .!!. .... | 1658 |  | O | 5
142 |  8 | 24 | 384 | !!.! !!!. .!!. .... | 1659 |  | E2 | 4
143 |  8 | 12 | 192 | .!!! !!!. .!!. .... | 1662 |  | E1 | 4
144 |  9 | 12 | 192 | !!!! !!!. .!!. .... | 1663 |  | O | 3
145 |  4 | 6 | 24 | .... !..! .!!. .... | 1680 | N(2,6) | E0 | 4
146 |  5 | 12 | 192 | !... !..! .!!. .... | 1681 |  | O | 3
147 |  6 | 12 | 192 | !!.. !..! .!!. .... | 1683 |  | E1 | 4
148 |  6 | 12 | 96 | .!!. !..! .!!. .... | 1686 |  | E2 | 2
149 |  7 | 12 | 192 | !!!. !..! .!!. .... | 1687 |  | O | 3
150 |  8 | 6 | 48 | !!!! !..! .!!. .... | 1695 |  | E0 | 4
151 |  5 | 6 | 96 | .... !!.! .!!. .... | 1712 |  | O | 3
152 |  6 | 24 | 384 | !... !!.! .!!. .... | 1713 |  | E2 | 4
153 |  6 | 12 | 192 | .!.. !!.! .!!. .... | 1714 |  | E1 | 4
154 |  7 | 24 | 384 | !!.. !!.! .!!. .... | 1715 |  | O | 5
155 |  6 | 12 | 192 | ..!. !!.! .!!. .... | 1716 |  | E3 | 4
156 |  7 | 24 | 384 | !.!. !!.! .!!. .... | 1717 |  | O | 5
157 |  7 | 12 | 192 | .!!. !!.! .!!. .... | 1718 |  | O | 3
158 |  8 | 24 | 384 | !!!. !!.! .!!. .... | 1719 |  | E2 | 4
159 |  7 | 12 | 192 | !..! !!.! .!!. .... | 1721 |  | O | 3
160 |  8 | 12 | 192 | !!.! !!.! .!!. .... | 1723 |  | E3 | 4
161 |  8 | 12 | 192 | !.!! !!.! .!!. .... | 1725 |  | E1 | 4
162 |  9 | 12 | 192 | !!!! !!.! .!!. .... | 1727 |  | O | 3
163 |  6 | 6 | 48 | .... !!!! .!!. .... | 1776 |  | E2 | 2
164 |  7 | 12 | 192 | !... !!!! .!!. .... | 1777 |  | O | 3
165 |  7 | 12 | 192 | .!.. !!!! .!!. .... | 1778 |  | O | 3
166 |  8 | 24 | 384 | !!.. !!!! .!!. .... | 1779 |  | E1 | 4
167 |  8 | 12 | 96 | .!!. !!!! .!!. .... | 1782 |  | E0 | 4
168 |  9 | 12 | 192 | !!!. !!!! .!!. .... | 1783 |  | O | 3
169 |  8 | 12 | 96 | !..! !!!! .!!. .... | 1785 |  | E0 | 4
170 |  9 | 12 | 192 | !!.! !!!! .!!. .... | 1787 |  | O | 3
171 | 10 | 12 | 96 | !!!! !!!! .!!. .... | 1791 |  | E2 | 2
172 |  8 | 3 | 48 | .!!. !!!. !!!. .... | 1910 |  | E4 | 4
173 |  9 | 3 | 48 | !!!. !!!. !!!. .... | 1911 |  | O | 5
174 |  7 | 6 | 96 | ...! !!!. !!!. .... | 1912 |  | O | 3
175 |  8 | 6 | 96 | !..! !!!. !!!. .... | 1913 |  | E4 | 4
176 |  8 | 12 | 192 | .!.! !!!. !!!. .... | 1914 |  | E3 | 4
177 |  9 | 12 | 192 | !!.! !!!. !!!. .... | 1915 |  | O | 5
178 |  9 | 6 | 96 | .!!! !!!. !!!. .... | 1918 |  | O | 5
179 | 10 | 6 | 96 | !!!! !!!. !!!. .... | 1919 |  | E2 | 4
180 |  6 | 12 | 96 | .... !!.! !!!. .... | 1968 |  | E3 | 2
181 |  7 | 24 | 384 | !... !!.! !!!. .... | 1969 |  | O | 3
182 |  8 | 12 | 192 | !!.. !!.! !!!. .... | 1971 |  | E2 | 4
183 |  7 | 24 | 384 | ..!. !!.! !!!. .... | 1972 |  | O | 3
184 |  8 | 24 | 384 | !.!. !!.! !!!. .... | 1973 |  | E4 | 4
185 |  8 | 24 | 384 | .!!. !!.! !!!. .... | 1974 |  | E3 | 4
186 |  9 | 24 | 384 | !!!. !!.! !!!. .... | 1975 |  | O | 5
187 |  8 | 12 | 192 | ..!! !!.! !!!. .... | 1980 |  | E2 | 4
188 |  9 | 24 | 384 | !.!! !!.! !!!. .... | 1981 |  | O | 5
189 | 10 | 12 | 192 | !!!! !!.! !!!. .... | 1983 |  | E3 | 4
190 |  6 | 6 | 48 | .... .!!! !!!. .... | 2016 |  | E4 | 2
191 |  7 | 12 | 192 | !... .!!! !!!. .... | 2017 |  | O | 3
192 |  7 | 12 | 192 | .!.. .!!! !!!. .... | 2018 |  | O | 3
193 |  8 | 24 | 384 | !!.. .!!! !!!. .... | 2019 |  | E3 | 4
194 |  8 | 6 | 96 | .!!. .!!! !!!. .... | 2022 |  | E2 | 4
195 |  9 | 12 | 192 | !!!. .!!! !!!. .... | 2023 |  | O | 5
196 |  8 | 6 | 96 | !..! .!!! !!!. .... | 2025 |  | E2 | 4
197 |  9 | 12 | 192 | !!.! .!!! !!!. .... | 2027 |  | O | 5
198 | 10 | 6 | 96 | !!!! .!!! !!!. .... | 2031 |  | E4 | 4
199 |  7 | 6 | 96 | .... !!!! !!!. .... | 2032 |  | O | 1
200 |  8 | 12 | 192 | !... !!!! !!!. .... | 2033 |  | E3 | 2
201 |  8 | 24 | 384 | .!.. !!!! !!!. .... | 2034 |  | E2 | 2
202 |  9 | 24 | 384 | !!.. !!!! !!!. .... | 2035 |  | O | 3
203 |  9 | 12 | 192 | .!!. !!!! !!!. .... | 2038 |  | O | 3
204 | 10 | 12 | 192 | !!!. !!!! !!!. .... | 2039 |  | E1 | 4
205 |  8 | 12 | 192 | ...! !!!! !!!. .... | 2040 |  | E1 | 2
206 |  9 | 12 | 192 | !..! !!!! !!!. .... | 2041 |  | O | 3
207 |  9 | 24 | 384 | .!.! !!!! !!!. .... | 2042 |  | O | 3
208 | 10 | 24 | 384 | !!.! !!!! !!!. .... | 2043 |  | E2 | 4
209 | 10 | 12 | 192 | .!!! !!!! !!!. .... | 2046 |  | E3 | 4
210 | 11 | 12 | 192 | !!!! !!!! !!!. .... | 2047 |  | O | 3
211 |  8 | 6 | 12 | .... !!!! !!!! .... | 4080 | N(3,2) | E0 | 0
212 |  9 | 6 | 96 | !... !!!! !!!! .... | 4081 |  | O | 1
213 | 10 | 12 | 96 | !!.. !!!! !!!! .... | 4083 |  | E1 | 2
214 | 10 | 6 | 48 | .!!. !!!! !!!! .... | 4086 |  | E2 | 2
215 | 11 | 6 | 96 | !!!. !!!! !!!! .... | 4087 |  | O | 3
216 | 12 | 6 | 24 | !!!! !!!! !!!! .... | 4095 |  | E0 | 4
217 |  6 | 1 | 8 | ...! .!!. .!!. !... | 5736 |  | E4 | 2
218 |  7 | 1 | 16 | !..! .!!. .!!. !... | 5737 |  | O | 1
219 |  7 | 4 | 64 | .!.! .!!. .!!. !... | 5738 |  | O | 3
220 |  8 | 4 | 64 | !!.! .!!. .!!. !... | 5739 |  | E3 | 2
221 |  8 | 6 | 96 | .!!! .!!. .!!. !... | 5742 |  | E2 | 4
222 |  9 | 6 | 96 | !!!! .!!. .!!. !... | 5743 |  | O | 3
223 |  9 | 4 | 64 | .!!! !!!. .!!. !... | 5758 |  | O | 5
224 | 10 | 4 | 64 | !!!! !!!. .!!. !... | 5759 |  | E1 | 4
225 |  5 | 1 | 16 | !... ...! .!!. !... | 5761 |  | O | 5
226 |  6 | 6 | 96 | !!.. ...! .!!. !... | 5763 |  | E2 | 4
227 |  6 | 12 | 96 | .!!. ...! .!!. !... | 5766 |  | E3 | 2
228 |  7 | 12 | 192 | !!!. ...! .!!. !... | 5767 |  | O | 3
229 |  6 | 4 | 64 | !..! ...! .!!. !... | 5769 |  | E3 | 4
230 |  7 | 12 | 192 | !!.! ...! .!!. !... | 5771 |  | O | 5
231 |  7 | 12 | 192 | .!!! ...! .!!. !... | 5774 |  | O | 3
232 |  8 | 12 | 192 | !!!! ...! .!!. !... | 5775 |  | E1 | 4
233 |  7 | 4 | 64 | .!!. !..! .!!. !... | 5782 |  | O | 1
234 |  8 | 4 | 64 | !!!. !..! .!!. !... | 5783 |  | E4 | 2
235 |  6 | 6 | 96 | ...! !..! .!!. !... | 5784 |  | E4 | 4
236 |  7 | 12 | 192 | !..! !..! .!!. !... | 5785 |  | O | 3
237 |  7 | 24 | 384 | .!.! !..! .!!. !... | 5786 |  | O | 3
238 |  8 | 24 | 384 | !!.! !..! .!!. !... | 5787 |  | E3 | 4
239 |  8 | 12 | 192 | .!!! !..! .!!. !... | 5790 |  | E2 | 2
240 |  9 | 12 | 192 | !!!! !..! .!!. !... | 5791 |  | O | 3
241 |  7 | 6 | 96 | !..! .!.! .!!. !... | 5801 |  | O | 3
242 |  8 | 6 | 96 | !!.! .!.! .!!. !... | 5803 |  | E4 | 4
243 |  7 | 12 | 192 | ..!! .!.! .!!. !... | 5804 |  | O | 5
244 |  8 | 24 | 384 | !.!! .!.! .!!. !... | 5805 |  | E2 | 4
245 |  8 | 24 | 384 | .!!! .!.! .!!. !... | 5806 |  | E3 | 4
246 |  9 | 24 | 384 | !!!! .!.! .!!. !... | 5807 |  | O | 5
247 |  8 | 12 | 192 | ..!! !!.! .!!. !... | 5820 |  | E1 | 4
248 |  9 | 12 | 192 | !.!! !!.! .!!. !... | 5821 |  | O | 5
249 |  9 | 12 | 192 | .!!! !!.! .!!. !... | 5822 |  | O | 3
250 | 10 | 12 | 192 | !!!! !!.! .!!. !... | 5823 |  | E2 | 4
251 |  8 | 4 | 64 | !..! .!!! .!!. !... | 5865 |  | E1 | 2
252 |  8 | 6 | 96 | .!.! .!!! .!!. !... | 5866 |  | E2 | 4
253 |  9 | 12 | 192 | !!.! .!!! .!!. !... | 5867 |  | O | 3
254 |  9 | 12 | 192 | .!!! .!!! .!!. !... | 5870 |  | O | 5
255 | 10 | 12 | 192 | !!!! .!!! .!!. !... | 5871 |  | E3 | 4
256 | 10 | 4 | 64 | .!!! !!!! .!!. !... | 5886 |  | E4 | 4
257 | 11 | 4 | 64 | !!!! !!!! .!!. !... | 5887 |  | O | 3
258 | 10 | 1 | 16 | .!!! !!!. !!!. !... | 6014 |  | E0 | 6
259 | 11 | 1 | 16 | !!!! !!!. !!!. !... | 6015 |  | O | 5
260 |  6 | 1 | 16 | !... ...! !!!. !... | 6017 |  | E0 | 6
261 |  7 | 6 | 96 | !!.. ...! !!!. !... | 6019 |  | O | 5
262 |  8 | 12 | 192 | !!!. ...! !!!. !... | 6023 |  | E2 | 4
263 |  7 | 4 | 64 | !..! ...! !!!. !... | 6025 |  | O | 5
264 |  8 | 12 | 192 | !!.! ...! !!!. !... | 6027 |  | E1 | 4
265 |  8 | 12 | 96 | .!!! ...! !!!. !... | 6030 |  | E0 | 4
266 |  9 | 12 | 192 | !!!! ...! !!!. !... | 6031 |  | O | 3
267 |  8 | 4 | 64 | .!!. !..! !!!. !... | 6038 |  | E3 | 2
268 |  9 | 4 | 64 | !!!. !..! !!!. !... | 6039 |  | O | 3
269 |  7 | 12 | 192 | ...! !..! !!!. !... | 6040 |  | O | 5
270 |  8 | 12 | 192 | !..! !..! !!!. !... | 6041 |  | E3 | 4
271 |  8 | 24 | 384 | .!.! !..! !!!. !... | 6042 |  | E2 | 4
272 |  9 | 24 | 384 | !!.! !..! !!!. !... | 6043 |  | O | 5
273 |  9 | 12 | 192 | .!!! !..! !!!. !... | 6046 |  | O | 3
274 | 10 | 12 | 192 | !!!! !..! !!!. !... | 6047 |  | E1 | 4
275 |  8 | 6 | 96 | !..! .!.! !!!. !... | 6057 |  | E2 | 4
276 |  9 | 6 | 96 | !!.! .!.! !!!. !... | 6059 |  | O | 3
277 |  8 | 24 | 384 | ..!! .!.! !!!. !... | 6060 |  | E1 | 4
278 |  9 | 24 | 384 | !.!! .!.! !!!. !... | 6061 |  | O | 5
279 |  9 | 24 | 384 | .!!! .!.! !!!. !... | 6062 |  | O | 3
280 | 10 | 24 | 384 | !!!! .!.! !!!. !... | 6063 |  | E2 | 4
281 |  9 | 12 | 192 | ..!! !!.! !!!. !... | 6076 |  | O | 5
282 | 10 | 12 | 192 | !.!! !!.! !!!. !... | 6077 |  | E0 | 6
283 | 10 | 12 | 192 | .!!! !!.! !!!. !... | 6078 |  | E1 | 4
284 | 11 | 12 | 192 | !!!! !!.! !!!. !... | 6079 |  | O | 5
285 |  8 | 4 | 32 | ...! .!!! !!!. !... | 6120 |  | E0 | 4
286 |  9 | 4 | 64 | !..! .!!! !!!. !... | 6121 |  | O | 3
287 |  9 | 12 | 192 | .!.! .!!! !!!. !... | 6122 |  | O | 3
288 | 10 | 12 | 192 | !!.! .!!! !!!. !... | 6123 |  | E1 | 4
289 | 10 | 12 | 192 | .!!! .!!! !!!. !... | 6126 |  | E2 | 4
290 | 11 | 12 | 192 | !!!! .!!! !!!. !... | 6127 |  | O | 5
291 | 11 | 4 | 64 | .!!! !!!! !!!. !... | 6142 |  | O | 5
292 | 12 | 4 | 64 | !!!! !!!! !!!. !... | 6143 |  | E3 | 4
293 |  8 | 4 | 32 | !!!. .!!! ...! !... | 6375 |  | E0 | 4
294 |  9 | 4 | 64 | !!!! .!!! ...! !... | 6383 |  | O | 3
295 | 10 | 4 | 32 | !!!! !!!! ...! !... | 6399 |  | E3 | 2
296 |  7 | 3 | 48 | !... .!!! !..! !... | 6625 |  | O | 5
297 |  8 | 12 | 192 | !!.. .!!! !..! !... | 6627 |  | E2 | 4
298 |  8 | 12 | 192 | .!!. .!!! !..! !... | 6630 |  | E1 | 2
299 |  9 | 12 | 192 | !!!. .!!! !..! !... | 6631 |  | O | 3
300 |  8 | 12 | 192 | !..! .!!! !..! !... | 6633 |  | E1 | 4
301 |  8 | 12 | 192 | .!.! .!!! !..! !... | 6634 |  | E2 | 4
302 |  9 | 24 | 384 | !!.! .!!! !..! !... | 6635 |  | O | 5
303 |  9 | 12 | 192 | .!!! .!!! !..! !... | 6638 |  | O | 3
304 | 10 | 12 | 192 | !!!! .!!! !..! !... | 6639 |  | E3 | 4
305 |  8 | 3 | 48 | !... !!!! !..! !... | 6641 |  | E4 | 4
306 |  9 | 12 | 192 | !!.. !!!! !..! !... | 6643 |  | O | 5
307 |  9 | 12 | 192 | .!!. !!!! !..! !... | 6646 |  | O | 3
308 | 10 | 12 | 192 | !!!. !!!! !..! !... | 6647 |  | E2 | 4
309 |  8 | 6 | 96 | ...! !!!! !..! !... | 6648 |  | E2 | 4
310 |  9 | 12 | 192 | !..! !!!! !..! !... | 6649 |  | O | 3
311 |  9 | 24 | 384 | .!.! !!!! !..! !... | 6650 |  | O | 5
312 | 10 | 24 | 384 | !!.! !!!! !..! !... | 6651 |  | E3 | 4
313 | 10 | 12 | 192 | .!!! !!!! !..! !... | 6654 |  | E4 | 4
314 | 11 | 12 | 192 | !!!! !!!! !..! !... | 6655 |  | O | 3
315 |  9 | 12 | 192 | .!!. !.!! !!.! !... | 7126 |  | O | 5
316 | 10 | 12 | 192 | !!!. !.!! !!.! !... | 7127 |  | E0 | 6
317 |  8 | 3 | 24 | ...! !.!! !!.! !... | 7128 |  | E0 | 4
318 |  9 | 12 | 192 | !..! !.!! !!.! !... | 7129 |  | O | 3
319 | 10 | 12 | 192 | !!.! !.!! !!.! !... | 7131 |  | E1 | 4
320 | 10 | 12 | 192 | .!!! !.!! !!.! !... | 7134 |  | E2 | 4
321 | 11 | 12 | 192 | !!!! !.!! !!.! !... | 7135 |  | O | 5
322 |  8 | 12 | 96 | ..!. .!!! !!.! !... | 7140 |  | E0 | 4
323 |  9 | 24 | 384 | !.!. .!!! !!.! !... | 7141 |  | O | 3
324 | 10 | 12 | 192 | !!!. .!!! !!.! !... | 7143 |  | E1 | 4
325 |  9 | 24 | 384 | ..!! .!!! !!.! !... | 7148 |  | O | 3
326 | 10 | 24 | 384 | !.!! .!!! !!.! !... | 7149 |  | E2 | 4
327 | 10 | 24 | 384 | .!!! .!!! !!.! !... | 7150 |  | E1 | 4
328 | 11 | 24 | 384 | !!!! .!!! !!.! !... | 7151 |  | O | 5
329 | 10 | 12 | 192 | ..!! !!!! !!.! !... | 7164 |  | E3 | 4
330 | 11 | 24 | 384 | !.!! !!!! !!.! !... | 7165 |  | O | 5
331 | 12 | 12 | 192 | !!!! !!!! !!.! !... | 7167 |  | E2 | 4
332 |  8 | 6 | 48 | !... .!!! .!!! !... | 7905 |  | E0 | 4
333 |  9 | 12 | 192 | !!.. .!!! .!!! !... | 7907 |  | O | 3
334 |  9 | 3 | 48 | .!!. .!!! .!!! !... | 7910 |  | O | 5
335 | 10 | 6 | 96 | !!!. .!!! .!!! !... | 7911 |  | E2 | 4
336 |  9 | 6 | 96 | !..! .!!! .!!! !... | 7913 |  | O | 3
337 | 10 | 12 | 192 | !!.! .!!! .!!! !... | 7915 |  | E1 | 4
338 | 10 | 3 | 48 | .!!! .!!! .!!! !... | 7918 |  | E0 | 6
339 | 11 | 6 | 96 | !!!! .!!! .!!! !... | 7919 |  | O | 5
340 |  9 | 6 | 96 | !... !!!! .!!! !... | 7921 |  | O | 3
341 | 10 | 24 | 384 | !!.. !!!! .!!! !... | 7923 |  | E2 | 4
342 | 10 | 12 | 192 | .!!. !!!! .!!! !... | 7926 |  | E3 | 4
343 | 11 | 12 | 192 | !!!. !!!! .!!! !... | 7927 |  | O | 5
344 | 10 | 12 | 192 | !..! !!!! .!!! !... | 7929 |  | E3 | 4
345 | 10 | 12 | 192 | .!.! !!!! .!!! !... | 7930 |  | E2 | 4
346 | 11 | 24 | 384 | !!.! !!!! .!!! !... | 7931 |  | O | 5
347 | 11 | 12 | 192 | .!!! !!!! .!!! !... | 7934 |  | O | 5
348 | 12 | 12 | 192 | !!!! !!!! .!!! !... | 7935 |  | E1 | 4
349 | 10 | 6 | 48 | !... !!!! !!!! !... | 8177 |  | E2 | 2
350 | 10 | 12 | 96 | .!.. !!!! !!!! !... | 8178 |  | E3 | 2
351 | 11 | 12 | 192 | !!.. !!!! !!!! !... | 8179 |  | O | 3
352 | 11 | 6 | 96 | .!!. !!!! !!!! !... | 8182 |  | O | 3
353 | 12 | 6 | 96 | !!!. !!!! !!!! !... | 8183 |  | E4 | 4
354 | 10 | 6 | 48 | ...! !!!! !!!! !... | 8184 |  | E4 | 2
355 | 11 | 6 | 96 | !..! !!!! !!!! !... | 8185 |  | O | 3
356 | 11 | 12 | 192 | .!.! !!!! !!!! !... | 8186 |  | O | 3
357 | 12 | 12 | 192 | !!.! !!!! !!!! !... | 8187 |  | E3 | 4
358 | 12 | 6 | 96 | .!!! !!!! !!!! !... | 8190 |  | E2 | 4
359 | 13 | 6 | 96 | !!!! !!!! !!!! !... | 8191 |  | O | 3
360 |  8 | 4 | 8 | !!.. ..!! ..!! !!.. | 15555 | N(3,3) | E0 | 0
361 |  9 | 4 | 64 | !!!. ..!! ..!! !!.. | 15559 |  | O | 1
362 | 10 | 4 | 32 | !!!! ..!! ..!! !!.. | 15567 |  | E1 | 2
363 | 10 | 12 | 96 | !!!. !.!! ..!! !!.. | 15575 |  | E2 | 2
364 | 10 | 12 | 96 | !!.! !.!! ..!! !!.. | 15579 |  | E3 | 2
365 | 11 | 12 | 192 | !!!! !.!! ..!! !!.. | 15583 |  | O | 3
366 | 12 | 12 | 48 | !!!! !!!! ..!! !!.. | 15615 |  | E0 | 4
367 | 10 | 4 | 64 | .!!. !.!! !.!! !!.. | 15830 |  | E3 | 4
368 | 11 | 4 | 64 | !!!. !.!! !.!! !!.. | 15831 |  | O | 3
369 | 10 | 6 | 96 | .!.! !.!! !.!! !!.. | 15834 |  | E4 | 4
370 | 11 | 12 | 192 | !!.! !.!! !.!! !!.. | 15835 |  | O | 3
371 | 11 | 12 | 192 | .!!! !.!! !.!! !!.. | 15838 |  | O | 5
372 | 12 | 12 | 192 | !!!! !.!! !.!! !!.. | 15839 |  | E3 | 4
373 | 11 | 12 | 192 | !.!! .!!! !.!! !!.. | 15853 |  | O | 5
374 | 12 | 12 | 192 | !!!! .!!! !.!! !!.. | 15855 |  | E2 | 4
375 | 12 | 6 | 96 | !.!! !!!! !.!! !!.. | 15869 |  | E2 | 4
376 | 12 | 12 | 192 | .!!! !!!! !.!! !!.. | 15870 |  | E1 | 4
377 | 13 | 12 | 192 | !!!! !!!! !.!! !!.. | 15871 |  | O | 3
378 | 12 | 4 | 16 | ..!! !!!! !!!! !!.. | 16380 |  | E0 | 4
379 | 13 | 4 | 64 | !.!! !!!! !!!! !!.. | 16381 |  | O | 3
380 | 14 | 4 | 32 | !!!! !!!! !!!! !!.. | 16383 |  | E1 | 2
381 |  8 | 1 | 2 | .!!. !..! !..! .!!. | 27030 | N(3,4) | E0 | 0
382 |  9 | 1 | 16 | !!!. !..! !..! .!!. | 27031 |  | O | 1
383 | 10 | 6 | 48 | !!!! !..! !..! .!!. | 27039 |  | E2 | 2
384 | 11 | 4 | 64 | !!!! !!.! !..! .!!. | 27071 |  | O | 3
385 | 12 | 4 | 16 | !!!! !!!! !..! .!!. | 27135 |  | E0 | 4
386 | 11 | 1 | 16 | !.!! !!.! !!.! .!!. | 27581 |  | O | 5
387 | 12 | 1 | 16 | !!!! !!.! !!.! .!!. | 27583 |  | E4 | 4
388 | 10 | 1 | 8 | .!!. !.!! !!.! .!!. | 27606 |  | E4 | 2
389 | 11 | 3 | 48 | !!!. !.!! !!.! .!!. | 27607 |  | O | 3
390 | 12 | 6 | 96 | !!!! !.!! !!.! .!!. | 27615 |  | E2 | 4
391 | 12 | 4 | 64 | !.!! !!!! !!.! .!!. | 27645 |  | E1 | 4
392 | 13 | 4 | 64 | !!!! !!!! !!.! .!!. | 27647 |  | O | 3
393 | 12 | 3 | 12 | .!!. !!!! !!!! .!!. | 28662 |  | E0 | 4
394 | 13 | 3 | 48 | !!!. !!!! !!!! .!!. | 28663 |  | O | 3
395 | 12 | 6 | 24 | !..! !!!! !!!! .!!. | 28665 |  | E0 | 4
396 | 13 | 6 | 96 | !!.! !!!! !!!! .!!. | 28667 |  | O | 3
397 | 14 | 6 | 48 | !!!! !!!! !!!! .!!. | 28671 |  | E2 | 2
398 | 14 | 4 | 32 | !!!! !!!! .!!! !!!. | 32511 |  | E3 | 2
399 | 14 | 1 | 8 | .!!! !!!! !!!! !!!. | 32766 |  | E4 | 2
400 | 15 | 1 | 16 | !!!! !!!! !!!! !!!. | 32767 |  | O | 1
401 | 16 | 1 | 1 | !!!! !!!! !!!! !!!! | 65535 | N(4,1) | E0 | 0

## Greatest big equivalence classes (ggbec)

[edit | edit source]

Table of the 39 ggbecs

| nonlin  | wec |  |  |  |

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|

0 | E0 | 32 | = | 25 |  | &0000ggbec 0

1 | O | 512 | = | 29 |  | &0001ggbec 1

2 | E1 | 1024 | = | 210 |  | &0003ggbec 3

2 | E2 | 1536 | = | 29 * 3  |  | &0006ggbec 6

3 | O | 3072 | = | 210 * 3  |  | &0007ggbec 7

4 | E0 | 192 | = | 26 * 3  |  | &0015ggbec 15

3 | O | 2048 | = | 211 |  | &0022ggbec 22

4 | E3 | 1024 | = | 210 |  | &0023ggbec 23

2 | E3 | 1024 | = | 210 |  | &0024ggbec 24

3 | O | 6144 | = | 211 * 3  |  | &0025ggbec 25

4 | E2 | 3072 | = | 210 * 3  |  | &0027ggbec 27

4 | E1 | 3072 | = | 210 * 3  |  | &0030ggbec 30

4 | E0 | 384 | = | 27 * 3  |  | &0060ggbec 60

4 | E0 | 128 | = | 27 |  | &0105ggbec 105

4 | E4 | 256 | = | 28 |  | &0278ggbec 278

5 | O | 512 | = | 29 |  | &0279ggbec 279

3 | O | 3072 | = | 210 * 3  |  | &0280ggbec 280

4 | E4 | 1536 | = | 29 * 3  |  | &0281ggbec 281

4 | E3 | 3072 | = | 210 * 3  |  | &0282ggbec 282

5 | O | 6144 | = | 211 * 3  |  | &0283ggbec 283

5 | O | 1536 | = | 29 * 3  |  | &0286ggbec 286

4 | E2 | 1536 | = | 29 * 3  |  | &0287ggbec 287

4 | E2 | 3072 | = | 210 * 3  |  | &0300ggbec 300

5 | O | 6144 | = | 211 * 3  |  | &0301ggbec 301

4 | E3 | 3072 | = | 210 * 3  |  | &0303ggbec 303

4 | E1 | 3072 | = | 210 * 3  |  | &0317ggbec 317

4 | E2 | 1536 | = | 29 * 3  |  | &0318ggbec 318

3 | O | 2048 | = | 211 |  | &0319ggbec 319

4 | E1 | 1024 | = | 210 |  | &0360ggbec 360

4 | E2 | 1536 | = | 29 * 3  |  | &0363ggbec 363

3 | O | 1536 | = | 29 * 3  |  | &0367ggbec 367

2 | E4 | 256 | = | 28 |  | &0383ggbec 383

4 | E0 | 128 | = | 27 |  | &0831ggbec 831

6 | E0 | 96 | = | 25 * 3  |  | &0854ggbec 854

6 | E0 | 384 | = | 27 * 3  |  | &0857ggbec 857

6 | E0 | 384 | = | 27 * 3  |  | &0874ggbec 874

4 | E0 | 96 | = | 25 * 3  |  | &1632ggbec 1632

4 | E0 | 192 | = | 26 * 3  |  | &1647ggbec 1647

6 | E0 | 32 | = | 25 |  | &6014ggbec 6014

## Walsh equivalence classes (wec)

[edit | edit source]

32768 = 215 |  | wec O

2048 = 211 |  | wec E0

8192 = 213 |  | wec E1

12288 = 212 * 3  |  | wec E2

8192 = 213 |  | wec E3

2048 = 211 |  | wec E4

wec E0 and wec E4

wec E1 and wec E3

## Ring count vectors (rcv)

[edit | edit source]

A step back:
The 16 2-ary Boolean functions correspond to the subsets of the nested set or hereditarily finite set V3 = P3({}) = { {} , {{}} , {{{}}} , {{},{{}}} }.
That is hard to read, so the nested sets are represented by nested rings of different size.

In the same way every 4-ary Boolean function corresponds to a subset of V4 = P4({}):

1111 1111 1111 1111

This set corresponds to the tautology. The cardinality of the subsets of V4 corresponds to the weight of the functions, in this case 16. Without the outer ring there are four different sizes of rings in these graphics. By counting also the smaller rings, the concept of weight can be refined, which leads to a 4-place ring count vector (rcv) for every 4-ary Boolean function. For the tautology it is (16,32,32,16).

For the next function the rcv is (8,16,16,8):

1001 1001 0011 1100

The vectors are not always so regular. For the next function it is (7,10,8,4):

1111 0110 0000 1000

Every set of 4-ary Boolean functions has a 5-place rcv where the first digit is the set's cardinality. E.g. the set that contains only the above-mentioned function has the rcv (1,7,10,8,4).

Sets of functions that are of some interest are equivalence classes. The last four digits in the rcvs of equivalence classes usually have the pattern n,2n,2n,n.

In the ggbec table above only the first digits are shown, because the rcvs have the pattern n,8n,16n,16n,8n. This is also true for the wec table, because a wec is a union of many ggbecs.

Every rcv has a leading one for the surrounding set, but for the sake of brevity it was omitted here. With it the sums are A116549.

## Subgroups of nimber addition

[edit | edit source]

See: Subgroups of nimber addition#Z24

## Bent functions

[edit | edit source]

There are 896 4-ary Bent functions,
which belong to four different greater big equivalence classes (gbecs).

Their nonlinearity is  2 4 − 1 − 2 4 2 − 1 = 8 − 2 = 6 {\displaystyle 2^{4-1}-2^{{\frac {4}{2}}-1}=8-2=6} and their Hamming weight is  2 4 − 1 ± 2 4 2 − 1 = 8 ± 2 {\displaystyle 2^{4-1}\pm 2^{{\frac {4}{2}}-1}=8\pm 2} .

Only the functions with Hamming weight 6 are shown. Those with Hamming weight 10 are their complements.

Belongs to BEC 391
with 16 functions. |  | The simplest example
of a 4-ary bent function:
x 1 ∧ x 2 ⊕ x 3 ∧ x 4 {\displaystyle x_{1}\land x_{2}~~\oplus ~~x_{3}\land x_{4}}
Belongs to BEC 381
with 3*16 functions. |  | Belongs to BEC 382
with 12*16 functions. |  | Belongs to BEC 383
with 12*16 functions.

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Big equivalence classes (becs)

| BEC 391
with 16 functions |  | BEC 381
with 3*16 = 48 functions |  | BEC 382
with 12*16 = 192 functions |  | BEC 383
with 12*16 = 192 functions

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|

(16 + 48 + 192 + 192) * 2 = 896

It's worth taking a look at the distribution of dots in the small matrices in the bec files.
They are all closely related to permuted Walsh matrices,
which is not the case for any other 4-ary Boolean functions.
Even more: Only the bent functions have 8 dots in every row (except the top row) of the small matrices.
Walsh permutation; bent functions

## About the bec files

[edit | edit source]

The files in this category describe big equivalence classes (becs).
They contain 24 sections, showing 16×16 sec matrices and a number between 0 and 23, representing a permutation of the four arguments.
The big matrices and the small matrices on the right show the same background colors representing binary numbers, but they differ in the dots.
In the big matrices the dots show which fields differ from the top row in the top matrix, while in the small matrices the dots show which fields differ from the top row of the matrix itself.
The numbers in the small left matrices show how the bits of the Boolean function in the top row of the top matrix are permuted. Their top rows are bit permutations.

The 24 small left matrices

M00 =

0     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15
1     0     3     2     5     4     7     6     9     8    11    10    13    12    15    14
2     3     0     1     6     7     4     5    10    11     8     9    14    15    12    13
3     2     1     0     7     6     5     4    11    10     9     8    15    14    13    12
4     5     6     7     0     1     2     3    12    13    14    15     8     9    10    11
5     4     7     6     1     0     3     2    13    12    15    14     9     8    11    10
6     7     4     5     2     3     0     1    14    15    12    13    10    11     8     9
7     6     5     4     3     2     1     0    15    14    13    12    11    10     9     8
8     9    10    11    12    13    14    15     0     1     2     3     4     5     6     7
9     8    11    10    13    12    15    14     1     0     3     2     5     4     7     6
10    11     8     9    14    15    12    13     2     3     0     1     6     7     4     5
11    10     9     8    15    14    13    12     3     2     1     0     7     6     5     4
12    13    14    15     8     9    10    11     4     5     6     7     0     1     2     3
13    12    15    14     9     8    11    10     5     4     7     6     1     0     3     2
14    15    12    13    10    11     8     9     6     7     4     5     2     3     0     1
15    14    13    12    11    10     9     8     7     6     5     4     3     2     1     0

M01 =

0     2     1     3     4     6     5     7     8    10     9    11    12    14    13    15
2     0     3     1     6     4     7     5    10     8    11     9    14    12    15    13
1     3     0     2     5     7     4     6     9    11     8    10    13    15    12    14
3     1     2     0     7     5     6     4    11     9    10     8    15    13    14    12
4     6     5     7     0     2     1     3    12    14    13    15     8    10     9    11
6     4     7     5     2     0     3     1    14    12    15    13    10     8    11     9
5     7     4     6     1     3     0     2    13    15    12    14     9    11     8    10
7     5     6     4     3     1     2     0    15    13    14    12    11     9    10     8
8    10     9    11    12    14    13    15     0     2     1     3     4     6     5     7
10     8    11     9    14    12    15    13     2     0     3     1     6     4     7     5
9    11     8    10    13    15    12    14     1     3     0     2     5     7     4     6
11     9    10     8    15    13    14    12     3     1     2     0     7     5     6     4
12    14    13    15     8    10     9    11     4     6     5     7     0     2     1     3
14    12    15    13    10     8    11     9     6     4     7     5     2     0     3     1
13    15    12    14     9    11     8    10     5     7     4     6     1     3     0     2
15    13    14    12    11     9    10     8     7     5     6     4     3     1     2     0

M02 =

0     1     4     5     2     3     6     7     8     9    12    13    10    11    14    15
1     0     5     4     3     2     7     6     9     8    13    12    11    10    15    14
4     5     0     1     6     7     2     3    12    13     8     9    14    15    10    11
5     4     1     0     7     6     3     2    13    12     9     8    15    14    11    10
2     3     6     7     0     1     4     5    10    11    14    15     8     9    12    13
3     2     7     6     1     0     5     4    11    10    15    14     9     8    13    12
6     7     2     3     4     5     0     1    14    15    10    11    12    13     8     9
7     6     3     2     5     4     1     0    15    14    11    10    13    12     9     8
8     9    12    13    10    11    14    15     0     1     4     5     2     3     6     7
9     8    13    12    11    10    15    14     1     0     5     4     3     2     7     6
12    13     8     9    14    15    10    11     4     5     0     1     6     7     2     3
13    12     9     8    15    14    11    10     5     4     1     0     7     6     3     2
10    11    14    15     8     9    12    13     2     3     6     7     0     1     4     5
11    10    15    14     9     8    13    12     3     2     7     6     1     0     5     4
14    15    10    11    12    13     8     9     6     7     2     3     4     5     0     1
15    14    11    10    13    12     9     8     7     6     3     2     5     4     1     0

M03 =

0     2     4     6     1     3     5     7     8    10    12    14     9    11    13    15
2     0     6     4     3     1     7     5    10     8    14    12    11     9    15    13
4     6     0     2     5     7     1     3    12    14     8    10    13    15     9    11
6     4     2     0     7     5     3     1    14    12    10     8    15    13    11     9
1     3     5     7     0     2     4     6     9    11    13    15     8    10    12    14
3     1     7     5     2     0     6     4    11     9    15    13    10     8    14    12
5     7     1     3     4     6     0     2    13    15     9    11    12    14     8    10
7     5     3     1     6     4     2     0    15    13    11     9    14    12    10     8
8    10    12    14     9    11    13    15     0     2     4     6     1     3     5     7
10     8    14    12    11     9    15    13     2     0     6     4     3     1     7     5
12    14     8    10    13    15     9    11     4     6     0     2     5     7     1     3
14    12    10     8    15    13    11     9     6     4     2     0     7     5     3     1
9    11    13    15     8    10    12    14     1     3     5     7     0     2     4     6
11     9    15    13    10     8    14    12     3     1     7     5     2     0     6     4
13    15     9    11    12    14     8    10     5     7     1     3     4     6     0     2
15    13    11     9    14    12    10     8     7     5     3     1     6     4     2     0

M04 =

0     4     1     5     2     6     3     7     8    12     9    13    10    14    11    15
4     0     5     1     6     2     7     3    12     8    13     9    14    10    15    11
1     5     0     4     3     7     2     6     9    13     8    12    11    15    10    14
5     1     4     0     7     3     6     2    13     9    12     8    15    11    14    10
2     6     3     7     0     4     1     5    10    14    11    15     8    12     9    13
6     2     7     3     4     0     5     1    14    10    15    11    12     8    13     9
3     7     2     6     1     5     0     4    11    15    10    14     9    13     8    12
7     3     6     2     5     1     4     0    15    11    14    10    13     9    12     8
8    12     9    13    10    14    11    15     0     4     1     5     2     6     3     7
12     8    13     9    14    10    15    11     4     0     5     1     6     2     7     3
9    13     8    12    11    15    10    14     1     5     0     4     3     7     2     6
13     9    12     8    15    11    14    10     5     1     4     0     7     3     6     2
10    14    11    15     8    12     9    13     2     6     3     7     0     4     1     5
14    10    15    11    12     8    13     9     6     2     7     3     4     0     5     1
11    15    10    14     9    13     8    12     3     7     2     6     1     5     0     4
15    11    14    10    13     9    12     8     7     3     6     2     5     1     4     0

M05 =

0     4     2     6     1     5     3     7     8    12    10    14     9    13    11    15
4     0     6     2     5     1     7     3    12     8    14    10    13     9    15    11
2     6     0     4     3     7     1     5    10    14     8    12    11    15     9    13
6     2     4     0     7     3     5     1    14    10    12     8    15    11    13     9
1     5     3     7     0     4     2     6     9    13    11    15     8    12    10    14
5     1     7     3     4     0     6     2    13     9    15    11    12     8    14    10
3     7     1     5     2     6     0     4    11    15     9    13    10    14     8    12
7     3     5     1     6     2     4     0    15    11    13     9    14    10    12     8
8    12    10    14     9    13    11    15     0     4     2     6     1     5     3     7
12     8    14    10    13     9    15    11     4     0     6     2     5     1     7     3
10    14     8    12    11    15     9    13     2     6     0     4     3     7     1     5
14    10    12     8    15    11    13     9     6     2     4     0     7     3     5     1
9    13    11    15     8    12    10    14     1     5     3     7     0     4     2     6
13     9    15    11    12     8    14    10     5     1     7     3     4     0     6     2
11    15     9    13    10    14     8    12     3     7     1     5     2     6     0     4
15    11    13     9    14    10    12     8     7     3     5     1     6     2     4     0

M06 =

0     1     2     3     8     9    10    11     4     5     6     7    12    13    14    15
1     0     3     2     9     8    11    10     5     4     7     6    13    12    15    14
2     3     0     1    10    11     8     9     6     7     4     5    14    15    12    13
3     2     1     0    11    10     9     8     7     6     5     4    15    14    13    12
8     9    10    11     0     1     2     3    12    13    14    15     4     5     6     7
9     8    11    10     1     0     3     2    13    12    15    14     5     4     7     6
10    11     8     9     2     3     0     1    14    15    12    13     6     7     4     5
11    10     9     8     3     2     1     0    15    14    13    12     7     6     5     4
4     5     6     7    12    13    14    15     0     1     2     3     8     9    10    11
5     4     7     6    13    12    15    14     1     0     3     2     9     8    11    10
6     7     4     5    14    15    12    13     2     3     0     1    10    11     8     9
7     6     5     4    15    14    13    12     3     2     1     0    11    10     9     8
12    13    14    15     4     5     6     7     8     9    10    11     0     1     2     3
13    12    15    14     5     4     7     6     9     8    11    10     1     0     3     2
14    15    12    13     6     7     4     5    10    11     8     9     2     3     0     1
15    14    13    12     7     6     5     4    11    10     9     8     3     2     1     0

M07 =

0     2     1     3     8    10     9    11     4     6     5     7    12    14    13    15
2     0     3     1    10     8    11     9     6     4     7     5    14    12    15    13
1     3     0     2     9    11     8    10     5     7     4     6    13    15    12    14
3     1     2     0    11     9    10     8     7     5     6     4    15    13    14    12
8    10     9    11     0     2     1     3    12    14    13    15     4     6     5     7
10     8    11     9     2     0     3     1    14    12    15    13     6     4     7     5
9    11     8    10     1     3     0     2    13    15    12    14     5     7     4     6
11     9    10     8     3     1     2     0    15    13    14    12     7     5     6     4
4     6     5     7    12    14    13    15     0     2     1     3     8    10     9    11
6     4     7     5    14    12    15    13     2     0     3     1    10     8    11     9
5     7     4     6    13    15    12    14     1     3     0     2     9    11     8    10
7     5     6     4    15    13    14    12     3     1     2     0    11     9    10     8
12    14    13    15     4     6     5     7     8    10     9    11     0     2     1     3
14    12    15    13     6     4     7     5    10     8    11     9     2     0     3     1
13    15    12    14     5     7     4     6     9    11     8    10     1     3     0     2
15    13    14    12     7     5     6     4    11     9    10     8     3     1     2     0

M08 =

0     1     4     5     8     9    12    13     2     3     6     7    10    11    14    15
1     0     5     4     9     8    13    12     3     2     7     6    11    10    15    14
4     5     0     1    12    13     8     9     6     7     2     3    14    15    10    11
5     4     1     0    13    12     9     8     7     6     3     2    15    14    11    10
8     9    12    13     0     1     4     5    10    11    14    15     2     3     6     7
9     8    13    12     1     0     5     4    11    10    15    14     3     2     7     6
12    13     8     9     4     5     0     1    14    15    10    11     6     7     2     3
13    12     9     8     5     4     1     0    15    14    11    10     7     6     3     2
2     3     6     7    10    11    14    15     0     1     4     5     8     9    12    13
3     2     7     6    11    10    15    14     1     0     5     4     9     8    13    12
6     7     2     3    14    15    10    11     4     5     0     1    12    13     8     9
7     6     3     2    15    14    11    10     5     4     1     0    13    12     9     8
10    11    14    15     2     3     6     7     8     9    12    13     0     1     4     5
11    10    15    14     3     2     7     6     9     8    13    12     1     0     5     4
14    15    10    11     6     7     2     3    12    13     8     9     4     5     0     1
15    14    11    10     7     6     3     2    13    12     9     8     5     4     1     0

M09 =

0     2     4     6     8    10    12    14     1     3     5     7     9    11    13    15
2     0     6     4    10     8    14    12     3     1     7     5    11     9    15    13
4     6     0     2    12    14     8    10     5     7     1     3    13    15     9    11
6     4     2     0    14    12    10     8     7     5     3     1    15    13    11     9
8    10    12    14     0     2     4     6     9    11    13    15     1     3     5     7
10     8    14    12     2     0     6     4    11     9    15    13     3     1     7     5
12    14     8    10     4     6     0     2    13    15     9    11     5     7     1     3
14    12    10     8     6     4     2     0    15    13    11     9     7     5     3     1
1     3     5     7     9    11    13    15     0     2     4     6     8    10    12    14
3     1     7     5    11     9    15    13     2     0     6     4    10     8    14    12
5     7     1     3    13    15     9    11     4     6     0     2    12    14     8    10
7     5     3     1    15    13    11     9     6     4     2     0    14    12    10     8
9    11    13    15     1     3     5     7     8    10    12    14     0     2     4     6
11     9    15    13     3     1     7     5    10     8    14    12     2     0     6     4
13    15     9    11     5     7     1     3    12    14     8    10     4     6     0     2
15    13    11     9     7     5     3     1    14    12    10     8     6     4     2     0

M10 =

0     4     1     5     8    12     9    13     2     6     3     7    10    14    11    15
4     0     5     1    12     8    13     9     6     2     7     3    14    10    15    11
1     5     0     4     9    13     8    12     3     7     2     6    11    15    10    14
5     1     4     0    13     9    12     8     7     3     6     2    15    11    14    10
8    12     9    13     0     4     1     5    10    14    11    15     2     6     3     7
12     8    13     9     4     0     5     1    14    10    15    11     6     2     7     3
9    13     8    12     1     5     0     4    11    15    10    14     3     7     2     6
13     9    12     8     5     1     4     0    15    11    14    10     7     3     6     2
2     6     3     7    10    14    11    15     0     4     1     5     8    12     9    13
6     2     7     3    14    10    15    11     4     0     5     1    12     8    13     9
3     7     2     6    11    15    10    14     1     5     0     4     9    13     8    12
7     3     6     2    15    11    14    10     5     1     4     0    13     9    12     8
10    14    11    15     2     6     3     7     8    12     9    13     0     4     1     5
14    10    15    11     6     2     7     3    12     8    13     9     4     0     5     1
11    15    10    14     3     7     2     6     9    13     8    12     1     5     0     4
15    11    14    10     7     3     6     2    13     9    12     8     5     1     4     0

M11 =

0     4     2     6     8    12    10    14     1     5     3     7     9    13    11    15
4     0     6     2    12     8    14    10     5     1     7     3    13     9    15    11
2     6     0     4    10    14     8    12     3     7     1     5    11    15     9    13
6     2     4     0    14    10    12     8     7     3     5     1    15    11    13     9
8    12    10    14     0     4     2     6     9    13    11    15     1     5     3     7
12     8    14    10     4     0     6     2    13     9    15    11     5     1     7     3
10    14     8    12     2     6     0     4    11    15     9    13     3     7     1     5
14    10    12     8     6     2     4     0    15    11    13     9     7     3     5     1
1     5     3     7     9    13    11    15     0     4     2     6     8    12    10    14
5     1     7     3    13     9    15    11     4     0     6     2    12     8    14    10
3     7     1     5    11    15     9    13     2     6     0     4    10    14     8    12
7     3     5     1    15    11    13     9     6     2     4     0    14    10    12     8
9    13    11    15     1     5     3     7     8    12    10    14     0     4     2     6
13     9    15    11     5     1     7     3    12     8    14    10     4     0     6     2
11    15     9    13     3     7     1     5    10    14     8    12     2     6     0     4
15    11    13     9     7     3     5     1    14    10    12     8     6     2     4     0

M12 =

0     1     8     9     2     3    10    11     4     5    12    13     6     7    14    15
1     0     9     8     3     2    11    10     5     4    13    12     7     6    15    14
8     9     0     1    10    11     2     3    12    13     4     5    14    15     6     7
9     8     1     0    11    10     3     2    13    12     5     4    15    14     7     6
2     3    10    11     0     1     8     9     6     7    14    15     4     5    12    13
3     2    11    10     1     0     9     8     7     6    15    14     5     4    13    12
10    11     2     3     8     9     0     1    14    15     6     7    12    13     4     5
11    10     3     2     9     8     1     0    15    14     7     6    13    12     5     4
4     5    12    13     6     7    14    15     0     1     8     9     2     3    10    11
5     4    13    12     7     6    15    14     1     0     9     8     3     2    11    10
12    13     4     5    14    15     6     7     8     9     0     1    10    11     2     3
13    12     5     4    15    14     7     6     9     8     1     0    11    10     3     2
6     7    14    15     4     5    12    13     2     3    10    11     0     1     8     9
7     6    15    14     5     4    13    12     3     2    11    10     1     0     9     8
14    15     6     7    12    13     4     5    10    11     2     3     8     9     0     1
15    14     7     6    13    12     5     4    11    10     3     2     9     8     1     0

M13 =

0     2     8    10     1     3     9    11     4     6    12    14     5     7    13    15
2     0    10     8     3     1    11     9     6     4    14    12     7     5    15    13
8    10     0     2     9    11     1     3    12    14     4     6    13    15     5     7
10     8     2     0    11     9     3     1    14    12     6     4    15    13     7     5
1     3     9    11     0     2     8    10     5     7    13    15     4     6    12    14
3     1    11     9     2     0    10     8     7     5    15    13     6     4    14    12
9    11     1     3     8    10     0     2    13    15     5     7    12    14     4     6
11     9     3     1    10     8     2     0    15    13     7     5    14    12     6     4
4     6    12    14     5     7    13    15     0     2     8    10     1     3     9    11
6     4    14    12     7     5    15    13     2     0    10     8     3     1    11     9
12    14     4     6    13    15     5     7     8    10     0     2     9    11     1     3
14    12     6     4    15    13     7     5    10     8     2     0    11     9     3     1
5     7    13    15     4     6    12    14     1     3     9    11     0     2     8    10
7     5    15    13     6     4    14    12     3     1    11     9     2     0    10     8
13    15     5     7    12    14     4     6     9    11     1     3     8    10     0     2
15    13     7     5    14    12     6     4    11     9     3     1    10     8     2     0

M14 =

0     1     8     9     4     5    12    13     2     3    10    11     6     7    14    15
1     0     9     8     5     4    13    12     3     2    11    10     7     6    15    14
8     9     0     1    12    13     4     5    10    11     2     3    14    15     6     7
9     8     1     0    13    12     5     4    11    10     3     2    15    14     7     6
4     5    12    13     0     1     8     9     6     7    14    15     2     3    10    11
5     4    13    12     1     0     9     8     7     6    15    14     3     2    11    10
12    13     4     5     8     9     0     1    14    15     6     7    10    11     2     3
13    12     5     4     9     8     1     0    15    14     7     6    11    10     3     2
2     3    10    11     6     7    14    15     0     1     8     9     4     5    12    13
3     2    11    10     7     6    15    14     1     0     9     8     5     4    13    12
10    11     2     3    14    15     6     7     8     9     0     1    12    13     4     5
11    10     3     2    15    14     7     6     9     8     1     0    13    12     5     4
6     7    14    15     2     3    10    11     4     5    12    13     0     1     8     9
7     6    15    14     3     2    11    10     5     4    13    12     1     0     9     8
14    15     6     7    10    11     2     3    12    13     4     5     8     9     0     1
15    14     7     6    11    10     3     2    13    12     5     4     9     8     1     0

M15 =

0     2     8    10     4     6    12    14     1     3     9    11     5     7    13    15
2     0    10     8     6     4    14    12     3     1    11     9     7     5    15    13
8    10     0     2    12    14     4     6     9    11     1     3    13    15     5     7
10     8     2     0    14    12     6     4    11     9     3     1    15    13     7     5
4     6    12    14     0     2     8    10     5     7    13    15     1     3     9    11
6     4    14    12     2     0    10     8     7     5    15    13     3     1    11     9
12    14     4     6     8    10     0     2    13    15     5     7     9    11     1     3
14    12     6     4    10     8     2     0    15    13     7     5    11     9     3     1
1     3     9    11     5     7    13    15     0     2     8    10     4     6    12    14
3     1    11     9     7     5    15    13     2     0    10     8     6     4    14    12
9    11     1     3    13    15     5     7     8    10     0     2    12    14     4     6
11     9     3     1    15    13     7     5    10     8     2     0    14    12     6     4
5     7    13    15     1     3     9    11     4     6    12    14     0     2     8    10
7     5    15    13     3     1    11     9     6     4    14    12     2     0    10     8
13    15     5     7     9    11     1     3    12    14     4     6     8    10     0     2
15    13     7     5    11     9     3     1    14    12     6     4    10     8     2     0

M16 =

0     4     8    12     1     5     9    13     2     6    10    14     3     7    11    15
4     0    12     8     5     1    13     9     6     2    14    10     7     3    15    11
8    12     0     4     9    13     1     5    10    14     2     6    11    15     3     7
12     8     4     0    13     9     5     1    14    10     6     2    15    11     7     3
1     5     9    13     0     4     8    12     3     7    11    15     2     6    10    14
5     1    13     9     4     0    12     8     7     3    15    11     6     2    14    10
9    13     1     5     8    12     0     4    11    15     3     7    10    14     2     6
13     9     5     1    12     8     4     0    15    11     7     3    14    10     6     2
2     6    10    14     3     7    11    15     0     4     8    12     1     5     9    13
6     2    14    10     7     3    15    11     4     0    12     8     5     1    13     9
10    14     2     6    11    15     3     7     8    12     0     4     9    13     1     5
14    10     6     2    15    11     7     3    12     8     4     0    13     9     5     1
3     7    11    15     2     6    10    14     1     5     9    13     0     4     8    12
7     3    15    11     6     2    14    10     5     1    13     9     4     0    12     8
11    15     3     7    10    14     2     6     9    13     1     5     8    12     0     4
15    11     7     3    14    10     6     2    13     9     5     1    12     8     4     0

M17 =

0     4     8    12     2     6    10    14     1     5     9    13     3     7    11    15
4     0    12     8     6     2    14    10     5     1    13     9     7     3    15    11
8    12     0     4    10    14     2     6     9    13     1     5    11    15     3     7
12     8     4     0    14    10     6     2    13     9     5     1    15    11     7     3
2     6    10    14     0     4     8    12     3     7    11    15     1     5     9    13
6     2    14    10     4     0    12     8     7     3    15    11     5     1    13     9
10    14     2     6     8    12     0     4    11    15     3     7     9    13     1     5
14    10     6     2    12     8     4     0    15    11     7     3    13     9     5     1
1     5     9    13     3     7    11    15     0     4     8    12     2     6    10    14
5     1    13     9     7     3    15    11     4     0    12     8     6     2    14    10
9    13     1     5    11    15     3     7     8    12     0     4    10    14     2     6
13     9     5     1    15    11     7     3    12     8     4     0    14    10     6     2
3     7    11    15     1     5     9    13     2     6    10    14     0     4     8    12
7     3    15    11     5     1    13     9     6     2    14    10     4     0    12     8
11    15     3     7     9    13     1     5    10    14     2     6     8    12     0     4
15    11     7     3    13     9     5     1    14    10     6     2    12     8     4     0

M18 =

0     8     1     9     2    10     3    11     4    12     5    13     6    14     7    15
8     0     9     1    10     2    11     3    12     4    13     5    14     6    15     7
1     9     0     8     3    11     2    10     5    13     4    12     7    15     6    14
9     1     8     0    11     3    10     2    13     5    12     4    15     7    14     6
2    10     3    11     0     8     1     9     6    14     7    15     4    12     5    13
10     2    11     3     8     0     9     1    14     6    15     7    12     4    13     5
3    11     2    10     1     9     0     8     7    15     6    14     5    13     4    12
11     3    10     2     9     1     8     0    15     7    14     6    13     5    12     4
4    12     5    13     6    14     7    15     0     8     1     9     2    10     3    11
12     4    13     5    14     6    15     7     8     0     9     1    10     2    11     3
5    13     4    12     7    15     6    14     1     9     0     8     3    11     2    10
13     5    12     4    15     7    14     6     9     1     8     0    11     3    10     2
6    14     7    15     4    12     5    13     2    10     3    11     0     8     1     9
14     6    15     7    12     4    13     5    10     2    11     3     8     0     9     1
7    15     6    14     5    13     4    12     3    11     2    10     1     9     0     8
15     7    14     6    13     5    12     4    11     3    10     2     9     1     8     0

M19 =

0     8     2    10     1     9     3    11     4    12     6    14     5    13     7    15
8     0    10     2     9     1    11     3    12     4    14     6    13     5    15     7
2    10     0     8     3    11     1     9     6    14     4    12     7    15     5    13
10     2     8     0    11     3     9     1    14     6    12     4    15     7    13     5
1     9     3    11     0     8     2    10     5    13     7    15     4    12     6    14
9     1    11     3     8     0    10     2    13     5    15     7    12     4    14     6
3    11     1     9     2    10     0     8     7    15     5    13     6    14     4    12
11     3     9     1    10     2     8     0    15     7    13     5    14     6    12     4
4    12     6    14     5    13     7    15     0     8     2    10     1     9     3    11
12     4    14     6    13     5    15     7     8     0    10     2     9     1    11     3
6    14     4    12     7    15     5    13     2    10     0     8     3    11     1     9
14     6    12     4    15     7    13     5    10     2     8     0    11     3     9     1
5    13     7    15     4    12     6    14     1     9     3    11     0     8     2    10
13     5    15     7    12     4    14     6     9     1    11     3     8     0    10     2
7    15     5    13     6    14     4    12     3    11     1     9     2    10     0     8
15     7    13     5    14     6    12     4    11     3     9     1    10     2     8     0

M20 =

0     8     1     9     4    12     5    13     2    10     3    11     6    14     7    15
8     0     9     1    12     4    13     5    10     2    11     3    14     6    15     7
1     9     0     8     5    13     4    12     3    11     2    10     7    15     6    14
9     1     8     0    13     5    12     4    11     3    10     2    15     7    14     6
4    12     5    13     0     8     1     9     6    14     7    15     2    10     3    11
12     4    13     5     8     0     9     1    14     6    15     7    10     2    11     3
5    13     4    12     1     9     0     8     7    15     6    14     3    11     2    10
13     5    12     4     9     1     8     0    15     7    14     6    11     3    10     2
2    10     3    11     6    14     7    15     0     8     1     9     4    12     5    13
10     2    11     3    14     6    15     7     8     0     9     1    12     4    13     5
3    11     2    10     7    15     6    14     1     9     0     8     5    13     4    12
11     3    10     2    15     7    14     6     9     1     8     0    13     5    12     4
6    14     7    15     2    10     3    11     4    12     5    13     0     8     1     9
14     6    15     7    10     2    11     3    12     4    13     5     8     0     9     1
7    15     6    14     3    11     2    10     5    13     4    12     1     9     0     8
15     7    14     6    11     3    10     2    13     5    12     4     9     1     8     0

M21 =

0     8     2    10     4    12     6    14     1     9     3    11     5    13     7    15
8     0    10     2    12     4    14     6     9     1    11     3    13     5    15     7
2    10     0     8     6    14     4    12     3    11     1     9     7    15     5    13
10     2     8     0    14     6    12     4    11     3     9     1    15     7    13     5
4    12     6    14     0     8     2    10     5    13     7    15     1     9     3    11
12     4    14     6     8     0    10     2    13     5    15     7     9     1    11     3
6    14     4    12     2    10     0     8     7    15     5    13     3    11     1     9
14     6    12     4    10     2     8     0    15     7    13     5    11     3     9     1
1     9     3    11     5    13     7    15     0     8     2    10     4    12     6    14
9     1    11     3    13     5    15     7     8     0    10     2    12     4    14     6
3    11     1     9     7    15     5    13     2    10     0     8     6    14     4    12
11     3     9     1    15     7    13     5    10     2     8     0    14     6    12     4
5    13     7    15     1     9     3    11     4    12     6    14     0     8     2    10
13     5    15     7     9     1    11     3    12     4    14     6     8     0    10     2
7    15     5    13     3    11     1     9     6    14     4    12     2    10     0     8
15     7    13     5    11     3     9     1    14     6    12     4    10     2     8     0

M22 =

0     8     4    12     1     9     5    13     2    10     6    14     3    11     7    15
8     0    12     4     9     1    13     5    10     2    14     6    11     3    15     7
4    12     0     8     5    13     1     9     6    14     2    10     7    15     3    11
12     4     8     0    13     5     9     1    14     6    10     2    15     7    11     3
1     9     5    13     0     8     4    12     3    11     7    15     2    10     6    14
9     1    13     5     8     0    12     4    11     3    15     7    10     2    14     6
5    13     1     9     4    12     0     8     7    15     3    11     6    14     2    10
13     5     9     1    12     4     8     0    15     7    11     3    14     6    10     2
2    10     6    14     3    11     7    15     0     8     4    12     1     9     5    13
10     2    14     6    11     3    15     7     8     0    12     4     9     1    13     5
6    14     2    10     7    15     3    11     4    12     0     8     5    13     1     9
14     6    10     2    15     7    11     3    12     4     8     0    13     5     9     1
3    11     7    15     2    10     6    14     1     9     5    13     0     8     4    12
11     3    15     7    10     2    14     6     9     1    13     5     8     0    12     4
7    15     3    11     6    14     2    10     5    13     1     9     4    12     0     8
15     7    11     3    14     6    10     2    13     5     9     1    12     4     8     0

M23 =

0     8     4    12     2    10     6    14     1     9     5    13     3    11     7    15
8     0    12     4    10     2    14     6     9     1    13     5    11     3    15     7
4    12     0     8     6    14     2    10     5    13     1     9     7    15     3    11
12     4     8     0    14     6    10     2    13     5     9     1    15     7    11     3
2    10     6    14     0     8     4    12     3    11     7    15     1     9     5    13
10     2    14     6     8     0    12     4    11     3    15     7     9     1    13     5
6    14     2    10     4    12     0     8     7    15     3    11     5    13     1     9
14     6    10     2    12     4     8     0    15     7    11     3    13     5     9     1
1     9     5    13     3    11     7    15     0     8     4    12     2    10     6    14
9     1    13     5    11     3    15     7     8     0    12     4    10     2    14     6
5    13     1     9     7    15     3    11     4    12     0     8     6    14     2    10
13     5     9     1    15     7    11     3    12     4     8     0    14     6    10     2
3    11     7    15     1     9     5    13     2    10     6    14     0     8     4    12
11     3    15     7     9     1    13     5    10     2    14     6     8     0    12     4
7    15     3    11     5    13     1     9     6    14     2    10     4    12     0     8
15     7    11     3    13     5     9     1    14     6    10     2    12     4     8     0

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