Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the field of coding theory, a coset leader is defined as 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 ...Täielik kirjeldus
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the field of coding theory, a coset leader is defined as 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.