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
刘才然, 宋贤梅
LIU Cai-ran, SONG Xian-mei
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。
中图分类号:
| [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. |
| [1] | 宋贤梅,熊蕾. Z2a+uZ2a 上线性码的MacWilliams恒等式及自对偶码[J]. 山东大学学报（理学版）, 2016, 51(2): 72-78. |
|
||
