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Permutation codes under the generalized Kendall- \(\tau \) metric are error-correcting codes with applications in rank modulation and related storage systems. Constructing permutation arrays is a challenging problem since even computing the distance between two permutations is NP-hard. This paper investigates (n, d)-permutation arrays (PAs) with prescribed length of permutations n and minimum generalized Kendall- \(\tau \) distance d. We determine exact values of T(n, d), the maximum size of a PA, for \(n=4\) and \(d=2,3\) . We develop algorithms for computing Kendall– \(\tau \) distances and constructing permutation arrays for \(n \le 11\) . An efficient testing procedure for (n, 2)-PAs is also presented.

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Constructing Permutation Codes Under the Generalized Kendall- \(\tau \) Metric

  • 会议论文

  • 发表日期：

    2026年

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  • Sergey Bereg,
  • Jack N. Truong

摘要

Permutation codes under the generalized Kendall- \(\tau \) metric are error-correcting codes with applications in rank modulation and related storage systems. Constructing permutation arrays is a challenging problem since even computing the distance between two permutations is NP-hard. This paper investigates (n, d)-permutation arrays (PAs) with prescribed length of permutations n and minimum generalized Kendall- \(\tau \) distance d. We determine exact values of T(n, d), the maximum size of a PA, for \(n=4\) and \(d=2,3\) . We develop algorithms for computing Kendall– \(\tau \) distances and constructing permutation arrays for \(n \le 11\) . An efficient testing procedure for (n, 2)-PAs is also presented.