Entry faithful 2-neighbour transitive codes

Neil I Gillespie, Daniel R. Hawtin, Michael Giudici, Cheryl E. Praeger

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
258 Downloads (Pure)

Abstract

We consider a code to be a subset of the vertex set of a Hamming graph. The set of s-neighbours of a code is the set of vertices, not in the code, at distance s from some codeword, but not distance less than s from any codeword. A 2-neighbour transitive code is a code which admits a group X of automorphisms which is transitive on the s-neighbours, for s=1,2, and transitive on the code itself. We give a classification of 2-neighbour transitive codes, with minimum distance δ≥5, for which X acts faithfully on the set of entries of the Hamming graph.
Original languageEnglish
Pages (from-to)549-564
Number of pages16
JournalDesigns, Codes and Cryptography
Volume79
Issue number3
Early online date2 Apr 2015
DOIs
Publication statusPublished - 1 Jun 2016

Keywords

  • Completely transitive codes
  • Regular codes
  • 2-Neighbour transitive codes
  • Automorphisms groups
  • Hamming graph

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