Entry-faithful 2-neighbour transitive codes

N.I. Gillespie, Michael Giudici, Dan Hawtin, Cheryl Praeger

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)

    Abstract

    © 2015, Springer Science+Business Media New York. We consider a code to be a subset of the vertex set of a Hamming graph. The set of (Formula presented.) -neighbours of a code is the set of vertices, not in the code, at distance (Formula presented.) from some codeword, but not distance less than (Formula presented.) from any codeword. A (Formula presented.) -neighbour transitive code is a code which admits a group (Formula presented.) of automorphisms which is transitive on the (Formula presented.) -neighbours, for (Formula presented.) , and transitive on the code itself. We give a classification of (Formula presented.) -neighbour transitive codes, with minimum distance (Formula presented.) , for which (Formula presented.) acts faithfully on the set of entries of the Hamming graph.
    Original languageEnglish
    Pages (from-to)549-564
    Number of pages16
    JournalDesigns, Codes, and Cryptography
    Volume79
    Issue number3
    Early online date2 Apr 2015
    DOIs
    Publication statusPublished - 1 Jun 2016

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