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A lower bound on permutation codes of distance \(n-1\)

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Abstract

A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length n and minimum distance \(n-1\). When such codes of length \(p+1\) are included as ingredients, we obtain a general lower bound \(M(n,n-1) \ge n^{1.0797}\) for large n, gaining a small improvement on the guarantee given from MOLS.

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Acknowledgements

We thank the referees for careful reading and helpful suggestions which improved the presentation.

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Authors and Affiliations

  1. Computer Science, University of Texas at Dallas, Richardson, TX, USA

    Sergey Bereg

  2. Mathematics and Statistics, University of Victoria, Victoria, BC, Canada

    Peter J. Dukes

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  1. Sergey Bereg
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  2. Peter J. Dukes
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Correspondence to Sergey Bereg.

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Communicated by C. J. Colbourn.

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Research of the first author is supported in part by NSF Award CCF-1718994. Research of the second author is supported by NSERC Grant 312595–2017.

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Bereg, S., Dukes, P.J. A lower bound on permutation codes of distance \(n-1\). Des. Codes Cryptogr. 88, 63–72 (2020). https://doi.org/10.1007/s10623-019-00670-5

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