Geodesic
Alphabet-almost-simple 2-neighbour-transitive codes
Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 345-357.

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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.
DOI : 10.26493/1855-3974.1240.515
Keywords: 2-neighbour-transitive, alphabet-almost-simple, automorphism groups, Hamming graph, completely transitive 
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Neil I. Gillespie; Daniel R. Hawtin. Alphabet-almost-simple 2-neighbour-transitive codes. Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 345-357. doi : 10.26493/1855-3974.1240.515. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1240.515/

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