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On self-dual cyclic codes over finite fields

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On self-dual cyclic codes over finite fields

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dc.contributor.author Jia, Yan
dc.contributor.author Ling, San
dc.contributor.author Xing, Chaoping
dc.date.accessioned 2012-02-03T03:01:15Z
dc.date.available 2012-02-03T03:01:15Z
dc.date.copyright 2011
dc.date.issued 2012-02-03
dc.identifier.citation Jia, Y., Ling, S. & Xing, C. (2011). On Self-Dual Cyclic Codes over Finite Fields. IEEE Transactions on Information Theory, 57(4), 2243 - 2251.
dc.identifier.uri http://hdl.handle.net/10220/7497
dc.description.abstract In coding theory, self-dual codes and cyclic codes are important classes of codes which have been extensively studied. The main objects of study in this paper are self-dual cyclic codes over finite fields, i.e., the intersection of these two classes. We show that self-dual cyclic codes of length n over BBFq exist if and only if n is even and q = 2m with m a positive integer. The enumeration of such codes is also investigated. When n and q are even, there is always a trivial self-dual cyclic code with generator polynomial xn/2+1. We, therefore, classify the existence of self-dual cyclic codes, for given n and q , into two cases: when only the trivial one exists and when two or more such codes exist. Given n and m , an easy criterion to determine which of these two cases occurs is given in terms of the prime factors of n, for most n . We also show that, over a fixed field, the latter case occurs more frequently as the length grows.
dc.language.iso en
dc.relation.ispartofseries IEEE transactions on information theory
dc.rights © 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: http://dx.doi.org/10.1109/TIT.2010.2092415 .
dc.subject DRNTU::Science::Mathematics.
dc.title On self-dual cyclic codes over finite fields
dc.type Journal Article
dc.contributor.school School of Physical and Mathematical Sciences
dc.identifier.doi http://dx.doi.org/10.1109/TIT.2010.2092415
dc.description.version Accepted version

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