2014/12/23 by Neil I. Gillespie, Gillespie, Neil I., Michael Giudici +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1412.7290
arXiv admin note: text overlap with arXiv:1208.0393
arxiv created 2014/12/23 · arxiv updated 2014/12/24
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.