Remoteness of permutation codes

Cameron, Peter J.; Gadouleau, Maximilien

Abstract

In this paper, we introduce a new parameter of a code, referred to as the remoteness, which can be viewed as a dual to the covering radius. Indeed, the remoteness is the minimum radius needed for a single ball to cover all codewords. After giving some general results about the remoteness, we then focus on the remoteness of permutation codes. We first derive upper and lower bounds on the minimum cardinality of a code with a given remoteness. We then study the remoteness of permutation groups. We show that the remoteness of transitive groups can only take two values, and we determine the remoteness of transitive groups of odd order. We finally show that the problem of determining the remoteness of a given transitive group is equivalent to determining the stability number of a related graph.

Citation

Cameron, P. J., & Gadouleau, M. (2012). Remoteness of permutation codes. European Journal of Combinatorics, 33(6), 1273-1285. https://doi.org/10.1016/j.ejc.2012.03.027

• Journal Article Type: Article
• Acceptance Date: Mar 9, 2012
• Publication Date: Aug 1, 2012
• Deposit Date: Mar 13, 2012
• Publicly Available Date: Feb 5, 2016
• Journal: European Journal of Combinatorics
• Print ISSN: 0195-6698
• Electronic ISSN: 1095-9971
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 6
• Pages: 1273-1285
• DOI: https://doi.org/10.1016/j.ejc.2012.03.027
• Public URL: https://durham-repository.worktribe.com/output/1502526