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环F_2+uF_2+vF_2+uvF_2上(1+uv)-循环码 被引量：2

(1+uv)-Cyclic Codes Over F_2+uF_2+vF_2+uvF_2
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摘要 该文定义了有限非链环R=F2+uF2+vF+uvF2上(1+uv)-循环码的相关概念,讨论了其与该环上循环码的关系,证明了此环上(1+uv)-循环码在关于齐次重量的等距Gray映射homf下的二元象是一个长为8n的4-准循环码,并由此映射得到了一些好的二元线性准循环码。 （1＋uv）-cyclic codes over F2＋uF2＋vF2＋uvF2 is defined, and the relations between （1＋uv）-cyclic codes and cyclic codes is discussed. It is proved that the binary image on isometric Gray map ？hom of a （1＋uv）-cyclic code of length n over R is a linear quasi-cyclic code of index 4 and of length 8n. Furthermore, some optimal binary linear quasi-cyclic codes are obtained.
作者 余海峰 朱士信 张霞
机构地区 合肥学院数学与物理系 合肥工业大学数学学院
出处 《电子与信息学报》 EI CSCD 北大核心 2014年第6期1419-1422,共4页 Journal of Electronics & Information Technology
基金 国家自然科学基金(60973125) 安徽高校省级自然科学基金(KJ2013Z276) 合肥学院科研发展重点基金(10KY01ZD)资助课题
关键词 循环码 (1+uv)-循环码 GRAY映射 准循环码 Cyclic codes （1＋uv）-cyclic code Gray map Quasi-cyclic code
分类号 TN911.22 [电子电信—通信与信息系统]
  • 相关文献

参考文献15

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二级参考文献14

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共引文献10

同被引文献21

  • 1朱士信,王立启.环F_p+uF_p+vF_p+uvF_p上的一类常循环码[J].数学物理学报（A辑）,2013,33(4):696-701. 被引量：7
  • 2Yildiz B,Karadenniz S.Linear codes over F2+uF2+vF2+uvF2[J].Designs,Codes and Cryptography,2010,54(1):61-81.
  • 3Yildiz B,Karadeniz S.Self-dual codes over F2+u F2+vF2+uvF2[J].Journal of the Franklin Institute,2010,347(10):1888-1894.
  • 4Yildiz B,Karadenniz S.Cyclic codes over F2+uF2+v F2+uvF2[J].Designs,Codes and Cryptography,2011,58(3):221-234.
  • 5Karadenniz S,Yildiz B.(1+v)-constacyclic codes over F2+uF2+vF2+uvF2[J].Journal of the Franklin Institute,2011,348(9):2625-2632.
  • 6Yildiz B,Karadenniz S.Linear codes over Z4+u Z4:MacWilliams identities,projections,and formally self-dual codes[J].Finite Fields and Their Applications,2014,27:24-40.
  • 7Kai Xiaoshan,Zhu Shixin,Li Ping.(1+λu)-Constacyclic codes over F p[u]/u m[J].Journal of the Franklin Institute,2010,347(5):751-762.
  • 8CENGELLENMIS Y. On the cyclic codes over F3 +vF3 [J]. International journal of algebra, 2010, 4(6) : 253 -259.
  • 9LIU X S, XU X F. Cyclic and negacyclic codes of length 2p' over Fpm + uFpm [ J ]~ Acta mathematica scientia,2014, 34 ( 3 ) : 829 - 839.
  • 10CENGELLENMIS Y, DOUGHERTY S T. Cyclic codes over Ak [ C] //Proceedings of ACCT 2012. Pomorie, Bulgaria, 2012. LIU X S, XU X F. Cyclic and negacyclic codes of length 2p' over Fpm + uFpm [ J ]. Acta mathematica scientia,2014, 34 ( 3 ) : 829 - 839.

引证文献2

二级引证文献1

电子与信息学报
2014年 第6期

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