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Subject Item: dbr:GV-linear-code
dbo:wikiPageWikiLink: dbr:Gilbert–Varshamov_bound_for_linear_codes
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dbo:wikiPageWikiLink: dbr:Gilbert–Varshamov_bound_for_linear_codes

Subject Item: dbr:Gilbert-Varshamov_bound_for_linear_codes
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Subject Item: dbr:Gilbert–Varshamov_bound_for_linear_codes
rdfs:label: Gilbert–Varshamov bound for linear codes
rdfs:comment: The Gilbert–Varshamov bound for linear codes is related to the general Gilbert–Varshamov bound, which gives a lower bound on the maximal number of elements in an error-correcting code of a given block length and minimum Hamming weight over a field . This may be translated into a statement about the maximum rate of a code with given length and minimum distance. The Gilbert–Varshamov bound for linear codes asserts the existence of q-ary linear codes for any relative minimum distance less than the given bound that simultaneously have high rate. The existence proof uses the probabilistic method, and thus is not constructive.The Gilbert–Varshamov bound is the best known in terms of relative distance for codes over alphabets of size less than 49. For larger alphabets, Goppa codes sometimes achie
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dbo:abstract: The Gilbert–Varshamov bound for linear codes is related to the general Gilbert–Varshamov bound, which gives a lower bound on the maximal number of elements in an error-correcting code of a given block length and minimum Hamming weight over a field . This may be translated into a statement about the maximum rate of a code with given length and minimum distance. The Gilbert–Varshamov bound for linear codes asserts the existence of q-ary linear codes for any relative minimum distance less than the given bound that simultaneously have high rate. The existence proof uses the probabilistic method, and thus is not constructive.The Gilbert–Varshamov bound is the best known in terms of relative distance for codes over alphabets of size less than 49. For larger alphabets, Goppa codes sometimes achieve an asymptotically better rate vs. distance tradeoff than is given by the Gilbert-Varshamov bound.
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