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  • ELUSIVE CODES IN HAMMING GRAPHS

  • Part of
  • DANIEL R. HAWTIN, NEIL I. GILLESPIE, CHERYL E. PRAEGER
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 88 / Issue 2 / October 2013
    Published online by Cambridge University Press:
    28 February 2013, pp. 286-296
    Print publication:
    October 2013
    • Article
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  • 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.