The covering radius of extreme binary 2-surjective codes |
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Authors: | Gerzson Kéri |
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Institution: | (1) Computer and Automation Research Institute, Hungarian Academy of Sciences, Kende u. 13–17, 1111 Budapest, Hungary |
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Abstract: | The covering radius of binary 2-surjective codes of maximum length is studied in the paper. It is shown that any binary 2-surjective
code of M codewords and of length has covering radius if M − 1 is a power of 2, otherwise . Two different combinatorial proofs of this assertion were found by the author. The first proof, which is written in the
paper, is based on an existence theorem for k-uniform hypergraphs where the degrees of its vertices are limited by a given upper bound. The second proof, which is omitted
for the sake of conciseness, is based on Baranyai’s theorem on l-factorization of a complete k-uniform hypergraph.
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Keywords: | Covering radius Divisibility of binomial coefficients Factorization Minimum distance Surjective code Uniform hypergraph |
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