On self-dual cyclic codes over finite fields

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On self-dual cyclic codes over finite fields

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Title: On self-dual cyclic codes over finite fields
Author: Jia, Yan; Ling, San; Xing, Chaoping
Copyright year: 2011
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.
Subject: DRNTU::Science::Mathematics.
Type: Journal Article
Series/ Journal Title: IEEE transactions on information theory
School: School of Physical and Mathematical Sciences
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 .
Version: Accepted version

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