摘要
针对环Fp+u Fp+v Fp+uv Fp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+u Fp+v Fp+uv Fp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+u Fp+v Fp+uv Fp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+u F3+v F3+uv F3上长为11的二次剩余码的幂等生成元的具体形式。
This paper investigated quadratic residue codes over Fp ＋ uFp ＋ vFp ＋ uvFp , where u^2 = u, v^2 = v, uv = vu and p is odd prime. At first, it introduced the basic knowledge of cyclic codes of length n over F~ ＋ uFp ＋ vFe ＋ UVFp, then obtained the structures of quadratic residue codes over Fp ＋ uFp ＋ vFp ＋ uvFp by applying their generating idempotents, and discussed the relations and dual properties between these codes and their extended codes. Finally, it gave the specific forms of generating idempotents of quadratic residue codes of length 11 over the ring F3 ＋ uF3 ＋vF3 ＋ uvF3.
出处
《计算机应用研究》
CSCD
北大核心
2015年第7期2136-2139,共4页
Application Research of Computers
基金
国家自然科学基金资助项目(61202068)
安徽省高校优秀青年人才基金重点项目(2012SQRL020ZD)
留学回国人员科技活动择优资助项目(05015133)
关键词
循环码
二次剩余码
幂等生成元
对偶码
扩展码
cyclic codes
quadratic-residue codes
generating idempotent
dual codes
extended codes
