Elusive codes in Hamming graphs

Authors

  • D. R. Hawtin University of Western Australia
  • N. I. Gillespie The University of Western Australia
  • C. E. Praeger The University of Western Australia

Keywords:

elusive codes, permutation codes, powerline communication, neighbour transitive codes, automorphism groups

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 our examples, we find that the alphabet size always divides the length of the code, and prove that there is no elusive pair for the smallest set of parameters for which this is not the case. We also pose several questions regarding elusive pairs. 10.1017/S0004972713000051

Author Biographies

N. I. Gillespie, The University of Western Australia

School of Mathematics and Statistics

C. E. Praeger, The University of Western Australia

School of Mathematics and Statistics

Published

2013-08-11

Issue

Vol. 88 No. 2 (2013)

Section

Articles
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