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山东大学学报(理学版) ›› 2014, Vol. 49 ›› Issue (10): 45-49.doi: 10.6040/j.issn.1671-9352.0.2014.260

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环Fl+vFl+v2Fl上的二次剩余码

刘才然, 宋贤梅   

  1. 安徽师范大学数学计算机科学学院, 安徽 芜湖 241003
  • 收稿日期:2014-06-05 出版日期:2014-10-20 发布日期:2014-11-10
  • 通讯作者: 宋贤梅(1977-),女,博士,副教授,研究方向为代数学,代数编码.E-mail:xianmeisongahnu@163.com E-mail:xianmeisongahnu@163.com
  • 作者简介:刘才然(1987-),女,硕士研究生,研究方向为代数编码.E-mail:liucairande@163.com
  • 基金资助:
    国家自然科学基金资助项目(11326062);安徽省教育厅重点研究项目(1408085QA01)

Quadratic residue codes over Fl+vFl+v2Fl

LIU Cai-ran, SONG Xian-mei   

  1. College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China
  • Received:2014-06-05 Online:2014-10-20 Published:2014-11-10

摘要: 用幂等生成元的形式定义了环R=Fl+vFl+v2Fl(v3=v,l 为奇素数)上的四种二次剩余码,探讨了这四种二次剩余码之间的关系。进一步地,得到了这四种二次剩余码与其对偶码之间的联系。

关键词: 二次剩余码, 幂等生成元, 对偶码

Abstract: Quadratic residue codes over the ring R=Fl+vFl+v2Fl are defined in terms of their idempotent generators, where v3=v and l is an odd prime. The relations among the four codes are discussed. Furthermore, the relations between the four codes and their dual codes are obtained.

Key words: generating idempotents, quadratic residue codes, dual code

中图分类号: 

  • TN911.22
[1] MACWILLIAMS F J, SLOANE N J A. The theory of error correcting code[M]. Amsterdam: North-Holland, 1977.
[2] WOLFMANN J. Negacyclic and cyclic codes over Z4[J]. IEEE Trans Inform Theory, 1999, 45(7):2527-2532.
[3] ABUALRUB T, OEHMKE R. On the generators of Z4 cyclic codes of length 2e[J]. IEEE Trans Inform Theory, 2003, 49(9):2126-2133.
[4] PlESS V, QIAN Z. Cyclic codes and quadratic residue codes over Z4[J]. IEEE Trans Inform Theory, 1996, 42(5):1596-1600.
[5] CHIU M H, YAU S S T, YU Y. Z8-cyclic codes and quadratic residue codes[J]. Advances in Appl Math, 2000, 25(1):12-33.
[6] 卢慧敏, 董学东, 李选海. Z2k上的二次剩余码 [J]. 应用数学学报, 2008, 31(2):257-265. LU Huimin, DONG Xuedong, LI Xuanhai. Quadratic Residue codes over Z2k[J]. Actc Mathematicae Applicatae Sinica, 2008, 31(2):257-265.
[7] KAYA A, YILDIZ B, SIAP I. New extremal binary self-dual codes of length 68 form quadratic residue codes over F2+uF2+u2F2, arXiv: 1308.0580, 2013.
[8] KAYA A, YILDIZ B, SIAP I. Quadratic residue codes over Fp+vFp and their Gray images, arXiv: 1305.4508, 2013.
[9] 曹德才, 朱士信. 环Fq+vFq+v2Fq上的常循环码[J]. 合肥工业大学学报:自然科学版, 2013, 36(12):1634-1536. CAO Decai, ZHU Shixin. Constacyclic codes over the ring Fq+vFq+v2Fq[J]. Journal of Hefei University of Technology: Natural Science, 2013, 36(12):1634-1536.
[10] 潘承洞, 潘承彪. 初等数论[M]. 北京:北京大学出版社, 1992. PAN Chengdong, PAN Chengbiao. Elementary number theory[M]. Bejing: Peking University Press, 1992.
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