环F2+uF2++uk-1F2上长为2S的(1+u)-常循环码的距离分布

施敏加; 杨善林; 朱士信

doi:10.3724/SP.J.1146.2008.01810

环F2+uF2++uk-1F2上长为2S的(1+u)-常循环码的距离分布

doi: 10.3724/SP.J.1146.2008.01810

施敏加^①②,,
杨善林^②,
朱士信^②

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出版历程
- 收稿日期: 2008-12-29
- 修回日期: 2009-06-19
- 刊出日期: 2010-01-19

The Distributions of Distances of (1+u)-Constacyclic Codes of Length 2S over F2+uF2++uk-1F2

Shi Min-jia^{①②
,},
Yang Shan-lin^②,
Zhu Shi-xin^②

摘要

摘要: 研究码字的距离分布是编码理论的一个重要研究方向。该文定义了环R=F2+uF2++uk-1F2上的Homogeneous重量，研究了环R上长为2S的(1+u)-常循环码的Hamming距离和Homogeneous距离。使用了有限环和域的理论，给出了环R上长为2S的(1+u)-常循环码和循环自对偶码的结构和码字个数。并利用该常循环码的结构，确定了环R上长为2S的(1+u)-常循环码的Hamming距离和Homogeneous距离分布。
- 常循环码; Hamming距离; Homogeneous距离
Abstract: In coding theory, it is important to study the distance distribution of codewords. The Homogeneous weight over ring R=F2+uF2++uk-1F2 is defined. Hamming distances and Homogeneous distances of (1+u)-constacyclic codes of length 2S over the ring R are studied. By means of the theory of finite rings, the structure of (1+u)-constacyclic codes of length 2S over R is also obtained. Especially, the structure and the size of cyclic self-dual codes over the ring are also given. Then, using the structure of such constacyclic codes, the distributions of the Hamming distances and Homogeneous distances of such constacyclic codes are determined.

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