| 环Fp uFp vFp uvFp上的二次剩余码 |
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| 引用本文： | 李倩倩,施敏加,葛茂荣.环Fp uFp vFp uvFp上的二次剩余码[J].计算机应用研究,2015,32(7). |
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| 作者姓名： | 李倩倩 施敏加 葛茂荣 |
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| 作者单位： | 安徽大学数学科学学院,合肥,230000 |
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| 基金项目： | 国家自然科学基金(No.61202068),安徽省高校优秀青年人才基金重点项目(No.2012SQRL0202D) |
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| 摘 要： | 针对环Fp+ uFp+ vFp+ uvFp上的二次剩余码进行了研究,其中u2=u,v2=v,uv=vu,p是一个奇素数.首先引入了环Fp+ uFp+vFp+ uvFp上长为n的循环码的相关知识,用幂等元的形式定义了环Fp+ uFp+vFp+uvFp上的二次剩余码,给出了其定义和性质,并讨论了它们与其扩展码之间的关系和对偶性质.最后,给出了环F3+uF3+vF3+uvF3上长为11的二次剩余码的幂等生成元的具体形式.
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| 关 键 词： | 循环码 二次剩余码 幂等生成元 对偶码 扩展码 |
| 收稿时间： | 6/4/2014 12:00:00 AM |
| 修稿时间： | 2015/5/28 0:00:00 |
Quadratic residue code over Fp uFp vFp uvFp |
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| Li Qianqian,Shi Minjia and Ge Maorong.Quadratic residue code over Fp uFp vFp uvFp[J].Application Research of Computers,2015,32(7). |
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| Authors: | Li Qianqian Shi Minjia and Ge Maorong |
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| Affiliation: | School of Mathematical Sciences of Anhui University. Hefei,School of Mathematical Sciences of Anhui University. Hefei,School of Mathematical Sciences of Anhui University. Hefei |
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| Abstract: | Quadratic residue codes over Fp uFp vFp uvFp is investigated in this article, where u2=u,v2=v,uv=vu, and p is odd prime. At first, the basic knowledge of cyclic codes of length n are introduced over Fp uFp vFp uvFp , then the structures of quadratic residue codes over Fp uFp vFp uvFp are obtained by applying their generating idempotents, and the relations and dual properties between these codes and their extended codes are discussed. Finally, the specific forms of generating idempotents of quadratic residue codes of length 11 over the ring F3 uF3 vF3 uvF3 is given. |
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| Keywords: | cyclic codes quadratic residue codes generating idempotent dual codes extended codes |
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