The Distributions of Distances of (1+u)-Constacyclic Codes of Length 2S over F2+uF2+…+uk-1F2
Shi Min-jia①②,Yang Shan-lin②,Zhu Shi-xin②
①School of Mathematics Sciences of Anhui University, Hefei 230039, China; ②Institute of Computer Network System, Hefei University of Technology, Hefei 230009, China
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 2Sover 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.
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 .
Shi Min-jia①②,Yang Shan-lin②,Zhu Shi-xin②. The Distributions of Distances of (1+u)-Constacyclic Codes of Length 2S over F2+uF2+…+uk-1F2. , 2010, 32(1): 112-116 .
2010, Vol. 32 
