Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (4): 720-728.

• Articles • Previous Articles     Next Articles

Chinese Product of Cyclic Codes over Zk

 TANG Yong-Sheng1,2, ZHU Shi-Xin1, SHI Min-Jia3   

  1. 1.School of Mathematics, Hefei University of Technology, Hefei 230009|
    2.Department of Mathematics, Hefei Normal University, Hefei 230601;
    3.Department of Mathematics, Anhui University, Hefei 230039
  • Received:2010-08-05 Revised:2011-11-30 Online:2012-08-25 Published:2012-08-25
  • Supported by:

    国家自然科学基金(60973125, 11126174)、安徽省高校优秀青年人才基金重点项目(2012SQRL020ZD)、合肥师范学院一般项目(2012kj10)和安徽省高校省级自然科学研究项目(KJ2010B171)资助

Abstract:

In this paper, we describe the Chinese Remainder Theorem for studying cyclic and dual cyclic codes over the ring Zk, where k=(∏i=1spi)m,   the pi are distinct primes and m is a positive integer, also with the condition that the code length n cannot be divided by pi. A necessary and sufficient condition for the existence of nontrivial cyclic self-dual codes is given. The upper bound of minimum distance of such cyclic codes is also obtained. Furthermore, we determine the minimal generator set and the rank of such cyclic codes.

Key words: The Chinese Remainder Theorem, Cyclic codes, Generator set

CLC Number: 

  • 94B05
Trendmd