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arXiv · 1412.7290

Entry-Faithful $2$-Neighbour Transitive Codes

Neil I. Gillespie·Michael Giudici·Daniel R. Hawtin·Cheryl E. Praeger
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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 $\delta\geq 5$, for which $X$ acts faithfully on the set of entries of the Hamming graph.

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Neil I. Gillespie, Michael Giudici, Daniel R. Hawtin, Cheryl E. Praeger. 2014-12-23. Entry-Faithful $2$-Neighbour Transitive Codes. https://arxiv.org/abs/1412.7290

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