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2019-03-20T04:17:47Z

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In [[coding theory]], a '''coset leader''' is a [[String (computer science)|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 [[Decoding methods#Syndrome decoding|syndrome]]. The corresponding coset leader is the most likely error pattern and we assume that ''v''+''u'' was the codeword sent.

==Source==

[http://wikipedia.org/ http://wikipedia.org/]
[[Category:Cryptography]]

Coset leader - Revision history

Admin: Created page with "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 no..."