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关于环F_p^m+uF_p^m+u²F_p^m上循环码的注记
刘修生

作者	单位
刘修生	湖北理工学院数理学院, 湖北黄石 435003

摘要:

本文研究了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码分类.通过建立环F_p^m+uF_p^m+u²F_p^m到环F_p^m+uF_p^m的同态,给出了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码的新分类方法.应用这种方法,得到了环F_p^m+uF_p^m+u²F_p^m长度为p^s的循环码的码词数.

关键词: 局部环循环码重根循环码码词数

DOI：

分类号:O157.4

基金项目:Supported by Scientific Research Foundation of Hubei Provincial Education Department of China (D20144401;B2015096) and the National Science Foundation of Hubei Polytechnic University of China (12xjz14A).

A NOTE ON CYCLIC CODES OVER F_p^m+uF_p^m+u²F_p^m

LIU Xiu-sheng

Abstract:

In this paper, we study cyclic codes of length p^s over the ring F_p^m+uF_p^m+u²F_p^m. By establishing the homomorphism from ring F_p^m+uF_p^m+u²F_p^m to F_p^m+uF_p^m+u²F_p^m, we give the new classify method for cyclic codes of length p^s over the ring F_p^m+uF_p^m+u²F_p^m. Using the method of the classify, we obtain the number of codewords in each of cyclic codes of length p^s over ring F_p^m+uF_p^m+u²F_p^m.

Key words: local ring cyclic codes repeated-root codes the number of codewords

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