Coset leader

In coding theory, a coset leader is a word of minimum weight in any particular coset \- that is, a word with the lowest amount of non-zero entries. Sometimes there are several words of equal minimum weight in a coset, and in that case, any one of those words may be chosen to be the coset leader. Coset leaders are used in the construction of a standard array for a linear code, which can then be used to decode received vectors. For a received vector y, the decoded message is y - e, where e is the coset leader of y. Coset leaders can also be used to construct a fast decoding strategy. For each coset leader u we calculate the syndrome uH′. When we receive v we evaluate vH′ and find the matching syndrome. The corresponding coset leader is the most likely error pattern and we assume that v+u was the codeword sent.

## References

* Hill, Raymond (1986). A First Course in Coding Theory. Oxford Applied Mathematics and Computing Science series. Oxford University Press. ISBN 978-0-19-853803-5. https://archive.org/details/firstcourseincod0000hill.

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