计算机工程与应用 ›› 2011, Vol. 47 ›› Issue (11): 26-29.

• 研究、探讨 • 上一篇    下一篇

F2+uF2+u2F2+u3F2上的循环码和自对偶码

闫国旗,辛小龙   

  1. 西北大学 数学系,西安 710127
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2011-04-11 发布日期:2011-04-11

Cyclic codes and self-dual codes over F2+uF2+u2F2+u3F2

YAN Guoqi,XIN Xiaolong   

  1. Department of Mathematics,Northwest University,Xi’an 710127,China
  • Received:1900-01-01 Revised:1900-01-01 Online:2011-04-11 Published:2011-04-11

摘要: 构造了一个含有16个元素的有限环,给出了这个有限环上码长为奇数的循环码的必要条件。然后给出了这个有限环上码长为奇数的循环码的一个生成多项式,得到了在这个环上的自对偶码存在的一个充分必要条件。

关键词: 有限环, 理想, 循环码, 自对偶码

Abstract: A finite ring with 16 elements is constructed and a necessary condition for a finite ring code with odd length becoming cyclic code is given.Furthermore,a generator polynomial of the finite ring code with odd length is obtained,and finally a necessary and sufficient condition for the existence of the self-dual codes of the finite ring is eventually proved.

Key words: finite ring, ideal, cyclic code, self-dual code