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Designs, Codes and Cryptography

Erschienen in:

01.06.2015

Permutation codes invariant under isometries

verfasst von: Ingo Janiszczak, Wolfgang Lempken, Patric R. J. Östergård, Reiner Staszewski

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2015

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Abstract

The symmetric group \(S_n\) on \(n\) letters is a metric space with respect to the Hamming distance. The corresponding isometry group is well known to be isomorphic to the wreath product \(S_n \wr S_2\). A subset of \(S_n\) is called a permutation code or a permutation array, and the largest possible size of a permutation code with minimum Hamming distance \(d\) is denoted by \(M(n, d)\). Using exhaustive search by computer on sets of orbits of isometry subgroups \(U\) we are able to determine serveral new lower bounds for \(M(n,d)\) for \(n \le 22\). The codes are given by the group \(U\) and representatives of the \(U\)-orbits.

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Titel: Permutation codes invariant under isometries
verfasst von: Ingo Janiszczak
Wolfgang Lempken
Patric R. J. Östergård
Reiner Staszewski
Publikationsdatum: 01.06.2015
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2015
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-014-9930-z

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