环F_p+vF_p上线性码的极小支座谱被引量：1

On the Minimum Support Hierarchy of Linear Codes over F_p+vF_p

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摘要基于环F_p+vF_p(v^2=v)上线性码的一种直和分解,利用环F_p+vF_p上的线性码的Torsion码,把环F_p+vF_p上的线性码的极小支座谱的确定归结于有限域上的情形;进一步探讨了环F_p+vF_p上的线性码的校验矩阵,利用该校验矩阵确定了环F_p+vF_p上的线性码的对偶码的极小支座谱;最后利用环上的线性码的极小支座谱,探讨了环F_p+vF_p上线性码的最小Hamming距离,并且给出了一个环F_p+vF_p上最小Hamming距离为d的线性码的构造方法,这里p是任一个素数,d是一个正整数. Based on the direct sum decomposition of linear codes over Fp ＋ vFp （ V2 = V ）, the minimum support hierarchy of linear codes over Fp ＋ vFp and their dual codes are studied by means of the Torsion codes and parity check matrice of these linear codes. With these results the Hamming distance of linear codes over Fp ＋ vFp are determined in terms of that of linear codes over the fmite field Fpand an explicit construction for linear codes over Fp ＋ vFp are given with the Hamming distance d, wherepis a prime and dis a positive integer.

作者张光辉

机构地区洛阳师范学院数学科学学院

出处《电子学报》 EI CAS CSCD 北大核心 2015年第8期1621-1626,共6页 Acta Electronica Sinica

基金国家自然科学基金(No.11171370) 河南省2014科技发展计划(No.144300510051) 2013年度河南省高等学校青年骨干教师资助计划(No.2013GGJS-152) 河南省教育厅自然科学基础研究项目(No.148110004)

关键词环Fp+vFp支座极小支座谱 HAMMING距离 Fp ＋ vFp support minimum support hierarchy Hamming distance

分类号 TN911.22 [电子电信—通信与信息系统]

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参考文献23

1Blake I F. Codes over certain rings[ J] .Information and Con- trol, 1972,20(4) :396 - 404.
2Blake I F. Codes over integer residue rings[ J]. Information and Control, 1975,29(4) :295 - 300.
3Hamrnons Jr A R, Kumar P V, Calderbank A R, Sloane N J A, So16 P. The Z4-1inearity of Kerdock, Preparata, Goethals and re- lated codes [J ]. IEEE Transactions on Information Theory, 1994,40(2) :301 - 319.
4Dinh H Q, Ltpez-Permouth S R. Cyclic and nega-cyclic codes over finite chain rings[ J ]. IEFE Transactions and Information Theory,2004,50(8) : 1728 - 1744.
5Dinh H Q. Constacyclic codes of length pS over Fp + uFp" [J]. Joth-'nal of Algebra,2010,324(5) :940- 950.
6Gulliver T A, Harada M. Codes over F3 + uF3 and improve- ments to the bounds on ternary linear codes[ J]. Designs Codes and Cryptography,2001,22( 1 ) :89 - 96.
7Kim J-L,Lee Y.Euclidean and Hem-titian self-dual MDS codes over large finite fields[ J] .Journal of Combinatorial Theory,Se- ries A,2(K, 105(1) :79 - 95.
8Kim J-L,Lee Y. Construction of MDS self-dual codes over Ga- lois rings[ J]. Designs Codes and Cr-yptography, 2007,45 (2) : 247 - 258.
9Kanwar P, L6pez-Permouth S R. Cyclic codes over the integers modulopm[j]. Finite Fields and Their Applications, 1997, 3 (4) : 334 - 352.
10Ling S, Blackford J. Zpk. 1-finear codes[ J]. IF, EF Transactions on Information Theory,2002,48(9) :2592 - 2605.

二级参考文献39

1余海峰,朱士信.环F_2+uF_2上线性码及其对偶码的Mac Williams恒等式[J].中国科学技术大学学报,2006,36(12):1285-1288. 被引量：17
2李平,朱士信.环F2＋uF2上长为2^e的循环码[J].电子与信息学报,2007,29(5):1124-1126. 被引量：16
3Taher Abualrub, Robert Oehmke. On the generators of cyclic codes of length 2e [J]. IEEE Trans Inform Theory, 2003,49 (9) :2126 - 2133.
4Xiaoshan Kai, Shixin Zhu. On the distances of cyclic codes of length 2e over Z4[J]..Discrete Mathematics,2010, 310( 1 ) : 12 - 20.
5H Q Dinh. Complete distances of all negacyclic codes of length 2^s over Z2^a [J ]. IEEE Trans Inform Theory, 2007,53 ( 1 ) : 147 - 161.
6H Q Dinh. Constacyclic codes of length 2s over Galois extension rings of F2 + uF2 [ J ]. IEEE Trans Inform Theory, 2009,55(4):1730 - 1740.
7F J MacWilliams. A theorem on the distribution of weights in a systematic code[ J]. Bell System Technical Journal, 1963,42 (2) :79 - 84.
8Z X Wan. _Quaternary Codes[M] .River Edge. N J:World Sci- entific Pub, 1997.
9A Ashikhmin. Generalized Hamming weights for Z4-linear codes[ A ]. Proceedings of IEEE International Symposium on Information Theory [ C ]. Trondheim Norway: IEEE Press, 1994. 306 - 306.
10A Ashikhmin. On generalized Hamming weights for Galois ring linear codes[ J]. Designs, Codes and Cryptography, 1998, 14 (2) : 107 - 126.