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The covering radius of extreme binary 2-surjective codes

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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 \(n = {M-1 \choose \left\lfloor(M-2)/2\right\rfloor}\) has covering radius \(\frac{n}{2} - 1\) if M − 1 is a power of 2, otherwise \(\left\lfloor\frac{n}{2}\right\rfloor\) . 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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Authors and Affiliations

  1. Computer and Automation Research Institute, Hungarian Academy of Sciences, Kende u. 13–17, 1111, Budapest, Hungary

    Gerzson Kéri

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  1. Gerzson Kéri
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Correspondence to Gerzson Kéri.

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Communicated by R.C. Mullin.

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Kéri, G. The covering radius of extreme binary 2-surjective codes. Des. Codes Cryptogr. 46, 191–198 (2008). https://doi.org/10.1007/s10623-007-9150-x

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  • DOI: https://doi.org/10.1007/s10623-007-9150-x

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