环Ｆ2+uＦ2上长为2e的循环码

李平; 朱士信

doi:10.3724/SP.J.1146.2005.01254

环Ｆ2+uＦ2上长为2e的循环码

doi: 10.3724/SP.J.1146.2005.01254

李平,
朱士信

基金项目:

国家自然科学基金(60673074)；教育部科学技术研究重点项目(107065)；安徽省高校青年教师科研资助计划重点项目(2006jql002 zd)和合肥工业大学科研发展基金项目(061003F)资助课题

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出版历程
- 收稿日期: 2005-10-08
- 修回日期: 2006-03-13
- 刊出日期: 2007-05-19

Cyclic Codes of Length 2e OverＦ2+uＦ2

摘要

摘要: 近十多年来，有限环上的循环码一直是编码研究者所关心的热点问题，本文证明了R[x]/xn-1 不是主理想环，其中R=Ｆ2+uＦ2，u2=0且n=2e。分3种情形讨论了环R[x]/xn-1中的非零理想，并给出了R上循环码的可以唯一确定的生成元的表达形式，同时给出了R上循环码的李距离的一个上界估计。
- 环Ｆ2+uＦ2；循环码；主理想；带余除法；李距离
Abstract: In the last ten more years, cyclic codes over finite rings have become a hot issue for coding theorists.It is proved that R[x]/xn-1 is not a principal ideal domain, where R=2+u2 with u2=0, and n=2e. The nonzero ideals of R[x]/xn-1 are discussed in three cases and the expressions of the uniquely determined generators of the cyclic codes are given. An estimate of upper bound of Lee distance of cyclic codes over R is also given.

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