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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Main Authors: Jia, Yan, Ling, San, Xing, Chaoping
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2012
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Online Access:https://hdl.handle.net/10356/94048
http://hdl.handle.net/10220/7497
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Institution: Nanyang Technological University
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spelling 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
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics
spellingShingle DRNTU::Science::Mathematics
Jia, Yan
Ling, San
Xing, Chaoping
On self-dual cyclic codes over finite fields
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Jia, Yan
Ling, San
Xing, Chaoping
format Article
author Jia, Yan
Ling, San
Xing, Chaoping
author_sort Jia, Yan
title 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
title_fullStr On self-dual cyclic codes over finite fields
title_full_unstemmed On self-dual cyclic codes over finite fields
title_sort on self-dual cyclic codes over finite fields
publishDate 2012
url https://hdl.handle.net/10356/94048
http://hdl.handle.net/10220/7497
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