数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 331-343.doi: 10.1016/S0252-9602(11)60233-6

• 论文 • 上一篇    下一篇

CYCLIC CODES OVER FORMAL POWER SERIES RINGS

Dougherty Steven T., 刘宏伟   

  1. Department of Mathematics, University of Scranton, Scranton, PA 18510, USA|Department of Mathematics, Huazhong Normal University, Wuhan 430079, China
  • 收稿日期:2008-05-15 修回日期:2009-06-03 出版日期:2011-01-20 发布日期:2011-01-20
  • 通讯作者: h_w_liu@yahoo.com.cn E-mail:doughertys1@scranton.edu; h_w_liu@yahoo.com.cn
  • 基金资助:

    The second author was supported by SRF for ROCS, SEM, the Key Project of Chinese Ministry of Education (108099), and CCNU Project (CCNU09Y01003)

CYCLIC CODES OVER FORMAL POWER SERIES RINGS

 Dougherty Steven T., LIU Hong-Wei   

  1. Department of Mathematics, University of Scranton, Scranton, PA 18510, USA|Department of Mathematics, Huazhong Normal University, Wuhan 430079, China
  • Received:2008-05-15 Revised:2009-06-03 Online:2011-01-20 Published:2011-01-20
  • Contact: h_w_liu@yahoo.com.cn E-mail:doughertys1@scranton.edu; h_w_liu@yahoo.com.cn
  • Supported by:

    The second author was supported by SRF for ROCS, SEM, the Key Project of Chinese Ministry of Education (108099), and CCNU Project (CCNU09Y01003)

摘要:

In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained.

关键词: Finite chain rings, cyclic codes, negacyclic codes,  γ-adic codes

Abstract:

In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained.

Key words: Finite chain rings, cyclic codes, negacyclic codes,  γ-adic codes

中图分类号: 

  • 94B05