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环F_p+uF_p+…+u^kF_p上的线性码和常循环码的Gray像 被引量：4

Gray images of linear codes and constacyclic codes over F_p+uF_p+…+u^kF_p
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摘要 定义了环(Fp+uFp+…+ukFp)n到Fppkn的一个Gray映射;给出Gray映射的几个性质,证明环Fp+uFp+…+ukFp上的长为n的线性码的Gray像仍是线性码;及该环上长为n的(1-uk)-循环码的Gray像是域Fp上的长为pkn、指数为pk-1的准循环码。 In this paper, the Gray map from （Fp＋uFp＋…＋u^kFp）^n to Fp^p^kn ositions of the map are given. It is shown that a code of the length n over Fp＋uFp＋…＋u^kFp is linear if and only if its Gray image is linear, and a code of the length n is cyclic if and only if its Gray image is a quasi-cyclic code over Fp of the index p^k-1 and the length p^k n.
作者 朱士信 吴波
机构地区 合肥工业大学理学院
出处 《合肥工业大学学报（自然科学版）》 CAS CSCD 北大核心 2006年第8期1049-1052,共4页 Journal of Hefei University of Technology：Natural Science
关键词 GRAY映射 线性码 常循环码 准循环码 Gray map linear code constacyclic code quasi-cyclic code
分类号 TN918 [电子电信—通信与信息系统]
  • 相关文献

参考文献11

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  • 5朱士信,童宏玺,钱建发.Z_p^(k+1)环上的循环码的Gray像[J].大学数学,2004,20(6):73-75. 被引量：3
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二级参考文献15

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共引文献4

同被引文献29

  • 1陈磊,陈卫红.Z_p^(k+1)环上的Quasi-Cyclic码[J].信息工程大学学报,2006,7(1):23-24. 被引量：1
  • 2Qian Jianfa, Zhang Lina, Zhu Shixin. Cyclic codes over Fp+uF^p+…+ u^kFp[J]. IEICE Trans Fundamentals, 2005, E88- A: 795-797.
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  • 7Tapia-Reeillas H, Vega G. A generalization of negacyclic codes[C]//Augot D, Cralet C. , Workshop on Coding and Cryptography,2001:519-529.
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  • 10Bonnecaze A, Udaya P. Cyclic codes and self-dual codes o- verFz-1-uFz [J]. IEEE Trans Inform Theory, 1999, 45: 1250-1255.

引证文献4

二级引证文献5

合肥工业大学学报（自然科学版）
2006年 第8期

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