Entry-Faithful $2$-Neighbour Transitive Codes

Abstract

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 $\delta \ge 5$, for which $X$ acts faithfully on the set of entries of the Hamming graph.

arXiv admin note: text overlap with arXiv:1208.0393

References in corpus (3)

• Characterisation of a family of neighbour transitive codes
• Classification of a family of completely transitive codes
• New families of completely transitive codes and distance transitive graphs