计算机工程与应用 ›› 2010, Vol. 46 ›› Issue (20): 84-85.DOI: 10.3778/j.issn.1002-8331.2010.20.023

• 网络、通信、安全 • 上一篇    下一篇

F2+uF2和Z4上循环码的Gray象

梁 华   

  1. 淮阴师范学院 数学科学学院,江苏 淮安 223300
  • 收稿日期:2009-12-31 修回日期:2010-03-31 出版日期:2010-07-11 发布日期:2010-07-11
  • 通讯作者: 梁 华

Gray images of cyclic codes over F2+uF2 and Z4

LIANG Hua   

  1. School of Mathematical Science,Huaiyin Teachers College,Huai’an,Jiangsu 223300,China
  • Received:2009-12-31 Revised:2010-03-31 Online:2010-07-11 Published:2010-07-11
  • Contact: LIANG Hua

摘要: 利用Gray映射Φ的性质,研究了环F2+uF2和Z4上的任意长循环码。证明了环F2+uF2上任意长码是循环码当且仅当它的Gray象是域F2上的准循环码,得到了Z4上任意长码是循环码的一个充分必要条件。特别的,环F2+uF2上长为n的线性循环码的Gray象是域F2上指标为2长为2n的线性准循环码,环Z4上长为n的线性循环码的Gray象是域F2上指标为2长为2n的准循环码。

关键词: 线性码, 循环码, 准循环码, Gray映射

Abstract: Based on the property of Gray map Φ,cyclic codes over F2+uF2 and Z4 are studied.It is proved that a code of arbitrary length over F2+uF2 is a cyclic code if and only if its Gray image is a quasi-cyclic code over F2,and a necessary and sufficient condition for a code of arbitrary length over Z4 to be a cyclic code is obtained.In particular,the Gray image of a linear cyclic code of length n over F2+uF2 is a linear quasi-cyclic code of index 2 and length 2n over F2,and the Gray image of a linear cyclic code of length n over Z4 is a quasi-cyclic code of index 2 and length 2n over F2.

Key words: linear code, cyclic code, quasi-cyclic code, Gray map

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