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Remoteness of permutation codes

Cameron, Peter J.; Gadouleau, Maximilien

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Peter J. Cameron


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.


Cameron, P. J., & Gadouleau, M. (2012). Remoteness of permutation codes. European Journal of Combinatorics, 33(6), 1273-1285.

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
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 33
Issue 6
Pages 1273-1285


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