Alphabet-almost-simple 2-neighbour-transitive codes

Neil I. Gillespie, Daniel R. Hawtin

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)345-357
    Number of pages13
    JournalArs Mathematica Contemporanea
    Volume14
    Issue number2
    Publication statusPublished - 2018

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  • Cite this

    Gillespie, N. I., & Hawtin, D. R. (2018). Alphabet-almost-simple 2-neighbour-transitive codes. Ars Mathematica Contemporanea, 14(2), 345-357.