On self-dual cyclic codes over finite fields
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 o...
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sg-ntu-dr.10356-940482023-02-28T19:38:05Z On self-dual cyclic codes over finite fields Jia, Yan Ling, San Xing, Chaoping School of Physical and Mathematical Sciences DRNTU::Science::Mathematics 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. Accepted version 2012-02-03T03:01:15Z 2019-12-06T18:49:54Z 2012-02-03T03:01:15Z 2019-12-06T18:49:54Z 2011 2011 Journal Article Jia, Y., Ling, S. & Xing, C. (2011). On Self-Dual Cyclic Codes over Finite Fields. IEEE Transactions on Information Theory, 57(4), 2243 - 2251. https://hdl.handle.net/10356/94048 http://hdl.handle.net/10220/7497 10.1109/TIT.2010.2092415 en IEEE transactions on information theory © 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 . application/pdf |
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DRNTU::Science::Mathematics Jia, Yan Ling, San Xing, Chaoping On self-dual cyclic codes over finite fields |
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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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Jia, Yan Ling, San Xing, Chaoping |
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Article |
author |
Jia, Yan Ling, San Xing, Chaoping |
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Jia, Yan |
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On self-dual cyclic codes over finite fields |
title_short |
On self-dual cyclic codes over finite fields |
title_full |
On self-dual cyclic codes over finite fields |
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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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on self-dual cyclic codes over finite fields |
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2012 |
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https://hdl.handle.net/10356/94048 http://hdl.handle.net/10220/7497 |
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