矩阵环 Mn×s(F l+v F l+…+v k-1 Fl)上线性码关于 重量的MacWillims恒等式

doi:10.3969/j.issn.0253-2778.2018.02.002

中国科学技术大学学报 ›› 2018, Vol. 48 ›› Issue (2): 97-104.DOI: 10.3969/j.issn.0253-2778.2018.02.002

矩阵环 Mn×s(F l+v F l+…+v k-1 Fl)上线性码关于重量的MacWillims恒等式

吴荣胜，施敏加，丁爽爽

安徽大学数学科学学院, 安徽合肥 23060

收稿日期:2017-01-10 修回日期:2017-12-13 出版日期:2018-02-28 发布日期:2018-02-28

MacWilliams identities of linear codes with respect to RT metric over Mn×s(F l+v F l+…+vk-1 l)

WU Rongsheng, SHI Minjia, DING Shuangshuang

School of Mathematical Sciences, Anhui University, Hefei 230601, China

Received:2017-01-10 Revised:2017-12-13 Online:2018-02-28 Published:2018-02-28
Contact: SHI Minjia
About author:WU Rongsheng, male, born in 1992, master. Research field: Algebraic coding. E-mail: wrs2510@163.com
Supported by:
Supported by National Natural Science Foundation of China (61672036), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (05015133), the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (2015D11), Key Projects of Support Program for Outstanding Young Talents in Colleges and Universities (gxyqZD2016008).

摘要/Abstract

摘要： 首先在交换环 R=

关键词: 重量计数器, MacWillims恒等式, 线性码, Gray 映射

Abstract: A new Gray map over the commutative ring R=

Key words: weight enumerator, MacWilliams identity, linear codes, Gray map

中图分类号:

TN911.22

吴荣胜，施敏加，丁爽爽. 矩阵环 Mn×s(F l+v F l+…+v k-1 Fl)上线性码关于重量的MacWillims恒等式[J]. 中国科学技术大学学报, 2018, 48(2): 97-104.

WU Rongsheng, SHI Minjia, DING Shuangshuang. MacWilliams identities of linear codes with respect to RT metric over Mn×s(F l+v F l+…+vk-1 l)[J]. Journal of University of Science and Technology of China, 2018, 48(2): 97-104.

参考文献

［1］
ROSENBLOOM M Y, TSFASMAN M A. Codes for the m-metric[J]. Problems of Information Transmission, 1997, 33(33): 55-63.
[2] DU W, XU H Q. MacWilliams identities of linear codes over ring Mn×s(R) with respect to the Rosenbloom-Tsfasman metric[J]. Information Technology Journal, 2012, 11(12): 1770-1775.

[3] WANG D D, SHI M J, LIU Y. MacWilliams identities of linear codes over a matrix ring with respect to Rosenbloom-Tsfasman metric[J]. International Journal of Information and Electronics Engineering, 2015, 5(3): 184-188.

[4] AMIT K S, ANURADHA S. MacWilliams identities for weight enumerators with respect to the RT metric[J]. Discrete Mathematics Algorithms and Applications, 2014, 6(2): 1450030.

[5] SIAP I. A MacWilliams type identity[J]. Turkish Journal of Mathematics, 2002, 26(4): 181-194.

[6] SIAP I. The complete weight enumerator for codes over Mn×s(Fq)[J]. Lecture Notes on Computer Sciences, 2001, 2260(1): 20-26.

[7] SIAP I, OZEN M. The complete weight enumerator for codes over Mn×s(R)[J]. Applied Mathematics Letters, 2004, 17(1): 65-69.

[8] SHI M J, LIU Y, SOL P. MacWilliams identities of linear codes with respect to RT metric over Mn×s(Fl + vFl + v2Fl)[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2014, E97-A(8): 1810-1813.

[9] SHI M J, SOL P, WU B. Cyclic codes and the weight enumerator of linear codes over F2 +vF2 +v2F2[J]. Applied and Computational Mathematics, 2013, 12(2): 247-255.

[10] MACWILLIAMS F J, SLOANE N J A. The Theory of Error Correcting Codes[M]. Amsterdam: North-Holland Publishing Co, 1997.

[11] ZHU S X, XU H Q, SHI M J. MacWilliams identity with respect to RT metric over ring Z4[J]. Acta Electronica Sinica, 2009, 37: 1116-1118.

()
(

[1]	丁健，李红菊. 环Fpm[u]/上一类常循环码的Gray像[J]. 中国科学技术大学学报, 2017, 47(7): 610-620.
[2]	管玥，刘艳，施敏加，卢振宇，吴波. 环 F q[u,v]/ 〈u2-1,v3-v,uv-vu〉上的斜循环码[J]. 中国科学技术大学学报, 2017, 47(10): 862-868.

矩阵环 Mn×s(F l+v F l+…+v k-1 Fl)上线性码关于重量的MacWillims恒等式

MacWilliams identities of linear codes with respect to RT metric over Mn×s(F l+v F l+…+vk-1 l)

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

编辑推荐

Metrics

本文评价

矩阵环 Mn×s(F l+v F l+…+v k-1 Fl)上线性码关于 重量的MacWillims恒等式

MacWilliams identities of linear codes with respect to RT metric over Mn×s(F l+v F l+…+vk-1 l)

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

编辑推荐

Metrics

本文评价

矩阵环 Mn×s(F l+v F l+…+v k-1 Fl)上线性码关于重量的MacWillims恒等式