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| 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 |
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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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Received: 29 December 2008
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Corresponding Authors:
Shi Min-jia
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2010, Vol. 32 
