数学物理学报 ›› 2013, Vol. 33 ›› Issue (4): 696-701.

• 论文 • 上一篇    下一篇

Fp+uFp+vFp+uvFp上的一类常循环码

朱士信|王立启   

  1. 合肥工业大学 数学学院 合肥 |230009
  • 收稿日期:2012-01-12 修回日期:2013-05-07 出版日期:2013-08-25 发布日期:2013-08-25
  • 基金资助:

    国家自然科学基金(60973125)资助.

A Class of Constacyclic Codes Over Fp+uFp+vFp+uvFp

 ZHU Shi-Xin, WANG Li-Qi   

  1. School of Mathematics, Hefei University of Technology, Hefei 230009
  • Received:2012-01-12 Revised:2013-05-07 Online:2013-08-25 Published:2013-08-25
  • Supported by:

    国家自然科学基金(60973125)资助.

摘要:

Fp+uFp+vFp+uvFp不是有限链环也不是主理想环. 文章研究了环R=Fp+uFp+vFp+uvFp上的(1+λu) -常循环码,其中Fpp元有限域, u2=v2=0, uv=vuλR中单位. 确定了任意长度该常循环的结构, 并利用结构性质构造了参数较好的p元线性码.

关键词: 常循环码, Gray映射, 齐次距离, Gray距离

Abstract:

The ring Fp+uFp+vFp+uvFp is not a finite chain ring and also not a principle ideal ring. In this paper, we study (1+λu)-constacyclic codes over the ring R=Fp+uFp+vFp+uvFp, where Fp is a finite field with p elements, u2=v2=0, uv=vu and λ is the unit in R. The structure of such constacyclic codes for an arbitrary length is determined. By using this structure, some p-ary linear codes with good parameters are also constructed.

Key words: Constacyclic codes, Gray map, Homogeneous distance, Gray distance

中图分类号: 

  • 94B05