Alphabet-almost-simple 2-neighbour-transitive codes

Authors

  • Neil I. Gillespie University of Bristol
  • Daniel R. Hawtin The University of Western Australia

DOI:

https://doi.org/10.26493/1855-3974.1240.515

Keywords:

2-neighbour-transitive, alphabet-almost-simple, automorphism groups, Hamming graph, completely transitive

Abstract

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.

Author Biography

Daniel R. Hawtin, The University of Western Australia

PhD student at the Centre for the Mathematics of Symmetry and Computation

Published

2017-09-30

Issue

Section

Articles