Repeated-root constacyclic codes of length ?/em> t p s and their dual codes

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• 作者：Anuradha Sharma
• 关键词：Constacyclic codes ; Self ; dual codes ; Self ; orthogonal codes ; 94B15
• 刊名：Cryptography and Communications
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：7
• 期：2
• 页码：229-255
• 全文大小：490 KB
• 参考文献：1. Apostal, T.M.: Introduction to Analytic Number Theory. Springer (1976)
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• 刊物类别：Computer Science
• 刊物主题：Coding and Information Theory
  Mathematics of Computing
  
• 出版者：Springer New York
• ISSN：1936-2455

文摘

Constacyclic codes form an interesting family of error-correcting codes due to their rich algebraic structure, and are generalizations of cyclic and negacyclic codes. In this paper, we classify repeated-root constacyclic codes of length ?/em> t p s over the finite field \(\mathbb {F}_{p^{m}}\) containing p m elements, where ?/em> ?1(mod 2), p are distinct primes and t, s, m are positive integers. Based upon this classification, we explicitly determine the algebraic structure of all repeated-root constacyclic codes of length ?/em> t p s over \(\mathbb {F}_{p^{m}}\) and their dual codes in terms of generator polynomials. We also observe that self-dual cyclic (negacyclic) codes of length ?/em> t p s over \(\mathbb {F}_{p^{m}}\) exist only when p = 2 and list all self-dual cyclic (negacyclic) codes of length ?/em> t 2 s over \(\mathbb {F}_{2^{m}}\) . We also determine all self-orthogonal cyclic and negacyclic codes of length ?/em> t p s over \(\mathbb {F}_{p^{m}}\) . To illustrate our results, we determine all constacyclic codes of length 175 over \(\mathbb {F}_{5}\) and all constacyclic codes of lengths 147 and 3087 over \(\mathbb {F}_{7}\) .