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Using permutation rational functions to obtain permutation arrays with large hamming distance

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Abstract

We consider permutation rational functions (PRFs), V(x)/U(x), where both V(x) and U(x) are polynomials over a finite field \(\mathbb {F}_q\). Permutation rational functions have been the subject of several recent papers. Let M(n, D) denote the maximum number of permutations on n symbols with pairwise Hamming distance D. Computing lower bounds for M(n, D) is the subject of current research with applications in error correcting codes. Using PRFs of specified degrees d we obtain improved lower bounds for\(M(q,q-k)\) for prime powers q and \(k \in \{5,6,7,8,9\}\), and for \(M(q+1,q-k)\) for prime powers q and \(k \in \{4,5,6,7,8,9\}\).

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Authors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, Box 830688, Richardson, TX, 75083, USA

    Sergey Bereg, Brian Malouf, Linda Morales, Thomas Stanley & I. Hal Sudborough

Authors
  1. Sergey Bereg
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  2. Brian Malouf
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  3. Linda Morales
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  4. Thomas Stanley
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  5. I. Hal Sudborough
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Corresponding author

Correspondence to I. Hal Sudborough.

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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.

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Bereg, S., Malouf, B., Morales, L. et al. Using permutation rational functions to obtain permutation arrays with large hamming distance. Des. Codes Cryptogr. 90, 1659–1677 (2022). https://doi.org/10.1007/s10623-022-01039-x

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  • DOI: https://doi.org/10.1007/s10623-022-01039-x

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