Notes 2 : Gilbert - Varshamov bound
نویسنده
چکیده
There is a natural greedy approach to construct a code of distance at least d: start with any codeword, and keep on adding codewords which have distance at least d from all previously chosen codewords, until we can proceed no longer. Suppose this procedure halts after picking a code C. Then Hamming balls in {0, 1, . . . , q−1}n of radius d−1 centered at the codewords of C must cover the whole space. (Otherwise, we can pick one more codeword which has distance at least d from every element of C, and the process would not have terminated.)
منابع مشابه
On Gilbert-Varshamov type bounds for Z2k linear codes
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تاریخ انتشار 2010