数学物理学报 ›› 2014, Vol. 34 ›› Issue (6): 1450-1455.

• 论文 • 上一篇    下一篇

Rk,q上的循环码

张晓燕   

  1. 湖北理工学院数理学院 湖北 黄石 |435003
  • 收稿日期:2013-10-08 修回日期:2014-04-06 出版日期:2014-12-25 发布日期:2014-12-25
  • 基金资助:

    湖北省教育厅自然科学基金(D20144401)资助

Cyclic Codes Over Rk,q

 ZHANG Xiao-Yan   

  1. School of Mathematics and Physics, Hubei Polytechnic University, Hubei Huangshi |435003
  • Received:2013-10-08 Revised:2014-04-06 Online:2014-12-25 Published:2014-12-25
  • Supported by:

    湖北省教育厅自然科学基金(D20144401)资助

摘要:

定义了一族环Rk,q, 研究了这族环Rk,q上的循环码. 证明了这族环Rk,q上循环码的Gray像是有限域Fq上2k -拟循环码.

关键词: 局部环, Gray映射, 循环码, l -拟循环码

Abstract:

A family of rings Rk,q is defined. Cyclic codes over a family of rings are studied. It is proved that the images of cyclic codes over these rings under Gray map are 2k-quasi-cyclic codes.

Key words: Local ring, Gray maps, Cyclic codes, l-Quasi-cyclic codes

中图分类号: 

  • 94B05