Designs, Codes and Cryptography

, Volume 86, Issue 5, pp 1095–1111 | Cite as

Constructing permutation arrays from groups

Article

Abstract

Let M(nd) be the maximum size of a permutation array on n symbols with pairwise Hamming distance at least d. We use various combinatorial, algebraic, and computational methods to improve lower bounds for M(nd). We compute the Hamming distances of affine semilinear groups and projective semilinear groups, and unions of cosets of AGL(1, q) and PGL(2, q) with Frobenius maps to obtain new, improved lower bounds for M(nd). We give new randomized algorithms. We give better lower bounds for M(nd) also using new theorems concerning the contraction operation. For example, we prove a quadratic lower bound for \(M(n,n-2)\) for all \(n\equiv 2 \pmod 3\) such that \(n+1\) is a prime power.

Keywords

Permutation codes Permutation arrays Finite fields Groups 

Mathematics Subject Classification

05A05 94B25 05E18 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Computer Science, Erik Jonsson School of Engineering and Computer ScienceUniversity of Texas at DallasRichardsonUSA
  2. 2.Department of MathematicsUniversity of WashingtonSeattleUSA

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