# 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.

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