数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 829-839.doi: 10.1016/S0252-9602(14)60053-9

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CYCLIC AND NEGACYCLIC CODES OF LENGTH 2ps OVER Fpm + uFpm

刘修生, 许小芳   

  1. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, China
  • 收稿日期:2013-04-26 修回日期:2013-10-24 出版日期:2014-05-20 发布日期:2014-05-20
  • 基金资助:

    The author is supported by the Natural Science Foundation of Hubei Province (D2014401) and the Natural Science Foundation of Hubei Polytechnic University (12xjz14A).

CYCLIC AND NEGACYCLIC CODES OF LENGTH 2ps OVER Fpm + uFpm

 LIU Xiu-Sheng, XU Xiao-Fang   

  1. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, China
  • Received:2013-04-26 Revised:2013-10-24 Online:2014-05-20 Published:2014-05-20
  • Supported by:

    The author is supported by the Natural Science Foundation of Hubei Province (D2014401) and the Natural Science Foundation of Hubei Polytechnic University (12xjz14A).

摘要:

In this article, we focus on cyclic and negacyclic codes of length 2ps over the ring R = Fpm + uFpm, where p is an odd prime. On the basis of the works of Dinh (in J.Algebra 324,940-950,2010), we use the Chinese Remainder Theorem to establish the alge-braic structure of cyclic and negacyclic codes of length 2ps over the ring Fpm +uFpm in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes.

关键词: Negacyclic codes, cyclic codes, repeated-root codes, finite chain ring, finite local ring

Abstract:

In this article, we focus on cyclic and negacyclic codes of length 2ps over the ring R = Fpm + uFpm, where p is an odd prime. On the basis of the works of Dinh (in J.Algebra 324,940-950,2010), we use the Chinese Remainder Theorem to establish the alge-braic structure of cyclic and negacyclic codes of length 2ps over the ring Fpm +uFpm in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes.

Key words: Negacyclic codes, cyclic codes, repeated-root codes, finite chain ring, finite local ring

中图分类号: 

  • 94B05