Alphabet-almost-simple 2-neighbour-transitive codes

Neil I. Gillespie, Daniel R. Hawtin

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

5 Citations (Scopus)
216 Downloads (Pure)


Let X be a subgroup of the full automorphism group of the Hamming graph H(m, q), and C a subset of the vertices of the Hamming graph. We say that C is an (X, 2)-neighbour-transitive code if X is transitive on C, as well as C1 and C2, the sets of vertices which are distance 1 and 2 from the code. It has been shown that, given an (X, 2)-neighbour-transitive code C, there exists a subgroup of X with a 2-transitive action on the alphabet; this action is thus almost-simple or affine. This paper completes the classification of (X, 2)-neighbour-transitive codes, with minimum distance at least 5, where the subgroup of X stabilising some entry has an almost-simple action on the alphabet in the stabilised entry. The main result of this paper states that the class of (X, 2) neighbour-transitive codes with an almost-simple action on the alphabet and minimum distance at least 3 consists of one infinite family of well known codes.

Original languageEnglish
Pages (from-to)345-357
Number of pages13
JournalArs Mathematica Contemporanea
Issue number2
Early online date30 Sept 2017
Publication statusPublished - 2018


  • 2-neighbour-transitive
  • Alphabet-almost-simple
  • Automorphism groups
  • Completely transitive
  • Hamming graph


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