| 环F2+uF2+…+uk-1F2上长为2S的(1+u)-常循环码的距离分布 |
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| 引用本文： | 施敏加,杨善林,朱士信.环F2+uF2+…+uk-1F2上长为2S的(1+u)-常循环码的距离分布[J].电子与信息学报,2010,32(1):112-116. |
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| 作者姓名： | 施敏加 杨善林 朱士信 |
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| 作者单位： | 安徽大学数学科学学院 合肥 230039; 合肥工业大学计算机网络系统研究所 合肥 230009 |
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| 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。
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| 关 键 词： | 常循环码 Hamming距离 Homogeneous距离 |
| 收稿时间： | 2008-12-29 |
| 修稿时间： | 2009-6-19 |
The Distributions of Distances of (1+u)-Constacyclic Codes of Length 2S over F2+uF2+…+uk-1F2 |
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| Shi Min-jia,Yang Shan-lin,Zhu Shi-xin.The Distributions of Distances of (1+u)-Constacyclic Codes of Length 2S over F2+uF2+…+uk-1F2[J].Journal of Electronics & Information Technology,2010,32(1):112-116. |
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| Authors: | Shi Min-jia Yang Shan-lin Zhu Shi-xin |
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| Affiliation: | School of Mathematics Sciences of Anhui University, Hefei 230039, China; Institute of Computer Network System, Hefei University of Technology, Hefei 230009, China |
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| 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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| Keywords: | Constacyclic code Hamming distance Homogeneous distance |
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