| 环F3+vF3上的循环码与常循环码 |
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| 引用本文： | 刘修生,许小芳,黄振华.环F3+vF3上的循环码与常循环码[J].数学杂志,2015,35(5):1115-1126. |
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| 作者姓名： | 刘修生 许小芳 黄振华 |
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| 作者单位： | 湖北理工学院数理学院, 湖北 黄石 435003,湖北理工学院数理学院, 湖北 黄石 435003,湖北师范学院数学与统计学院, 湖北 黄石 435002 |
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| 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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| 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.
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| 关 键 词： | 循环码 常循环码 Gray映射 生成多项式 |
| 收稿时间： | 2013/9/22 0:00:00 |
| 修稿时间： | 2013/11/6 0:00:00 |
CYCLIC AND CONSTACYCLIC CODES OVER F3 + vF3 |
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| LIU Xiu-sheng,XU Xiao-fang and HUANG Zheng-hua.CYCLIC AND CONSTACYCLIC CODES OVER F3 + vF3[J].Journal of Mathematics,2015,35(5):1115-1126. |
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| Authors: | LIU Xiu-sheng XU Xiao-fang and HUANG Zheng-hua |
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| Institution: | School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, China,School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, China and College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China |
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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. |
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| Keywords: | cyclic codes constacyclic codes Gray map generator polynomial |
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