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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 ==
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抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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