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| 摘要: |
| 本文研究了环F3+vF3上的循环码与常循环码.通过环F3+vF3与域F3上的循环码之间关系,证明了环F3+vF3上循环码是由一个多项式生成的.最后,用类似的方法,得到了环F3+vF3上v-常循环码也是由一个多项式生成的. |
| 关键词: 循环码 常循环码 Gray映射 生成多项式 |
| DOI： |
| 分类号:O157.4 |
| 基金项目:Supported by Scientiflc Research Foundation of Hubei Provincial Education Department of China (B2013069);National Science Foundation of Hubei Polytechnic University of China (12xjz14A) |
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| CYCLIC AND CONSTACYCLIC CODES OVER F3 + vF3 |
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LIU Xiu-sheng,XU Xiao-fang,HUANG Zheng-hua
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| Abstract: |
| In this paper, we focus on cyclic and constacyclic codes over the ring F3+vF3(v2=1), which is not a finite chain ring. We study the relationship between cyclic codes over F3 + vF3 and ternary cyclic codes, and prove that cyclic codes over the ring are generated by a polynomial over F3 + vF3. Then, using similar method, we obtain the generator polynomial of v-constacyclic codes. |
| Key words: cyclic codes constacyclic codes Gray map generator polynomial |
