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Remoteness of permutation codes.

Cameron, Peter J. and Gadouleau, Maximilien (2012) 'Remoteness of permutation codes.', European journal of combinatorics., 33 (6). pp. 1273-1285.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.ejc.2012.03.027
Publisher statement:© 2012 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:09 March 2012
Date deposited:05 February 2016
Date of first online publication:August 2012
Date first made open access:No date available

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