Error-correcting codes from permutation groups
نویسندگان
چکیده
منابع مشابه
Error-correcting codes from permutation groups
We replace the usual setting for error-correcting codes (i.e. vector spaces over finite fields) with that of permutation groups. We give an algorithm which uses a combinatorial structure which we call an uncovering-by-bases, related to covering designs, and construct some examples of these. We also analyse the complexity of the algorithm. We then formulate a conjecture about uncoverings-by-base...
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Permutation Groups, Error-Correcting Codes and Uncoverings Robert F. Bailey School of Mathematical Sciences Queen Mary, University of London Mile End Road, London E1 4NS United Kingdom [email protected] We replace the traditional setting of error-correcting codes (namely vector spaces over finite fields) with that of permutation groups, using permutations written in list form as the codewor...
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Let A2(n, d) be the maximum size of a binary code of length n and minimum distance d. In this paper we present the following new lower bounds: A2(18, 4) ≥ 5632, A2(21, 4) ≥ 40960, A2(22, 4) ≥ 81920, A2(23, 4) ≥ 163840, A2(24, 4) ≥ 327680, A2(24, 10) ≥ 136, and A2(25, 6) ≥ 17920. The new lower bounds are a result of a systematic computer search over transitive permutation groups.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.12.027