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ELUSIVE CODES IN HAMMING GRAPHS

Part of: Theory of error-correcting codes and error-detecting codes Algebraic combinatorics

Published online by Cambridge University Press:  28 February 2013

DANIEL R. HAWTIN ,
NEIL I. GILLESPIE  and
CHERYL E. PRAEGER
DANIEL R. HAWTIN*
Affiliation:
The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia email neil.gillespie@uwa.edu.aucheryl.praeger@uwa.edu.au
NEIL I. GILLESPIE
Affiliation:
The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia email neil.gillespie@uwa.edu.aucheryl.praeger@uwa.edu.au
CHERYL E. PRAEGER
Affiliation:
The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia email neil.gillespie@uwa.edu.aucheryl.praeger@uwa.edu.au Also affiliated with King Abdulaziz University, Jeddah, Saudi Arabia email cheryl.praeger@uwa.edu.au
*
✉dan.hawtin@gmail.com
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Abstract

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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.

Keywords

elusive codespermutation codespowerline communicationneighbour transitive codesautomorphism groups

MSC classification

Secondary: 94B60: Other types of codes 05E18: Group actions on combinatorial structures
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 286 - 296
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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