Elusive codes in hamming graphs

Dan Hawtin, Neil Gillespie, Cheryl Praeger

    Research output: Contribution to journalArticle

    Abstract

    We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In these examples, the alphabet size always divides the length of the code. We show that there is no elusive pair for the smallest set of parameters that does not satisfy this condition. We also pose several questions regarding elusive pairs. © 2013 Australian Mathematical Publishing Association Inc.
    Original languageEnglish
    Pages (from-to)286-296
    JournalBulletin of the Australian Mathematical Society
    Volume88
    Issue number2
    DOIs
    Publication statusPublished - 2013

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