环Mn×s(Rk)上线性码关于RT距离的MacWilliams恒等式

doi:10.3969/j.issn.0253-2778.2015.01.006

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (1): 34-39.DOI: 10.3969/j.issn.0253-2778.2015.01.006

• 论著 • 上一篇

环Mn×s(Rk)上线性码关于RT距离的MacWilliams恒等式

姚婷，施敏加，刘艳

安徽大学数学科学学院,安徽合肥 230601

收稿日期:2014-06-05 修回日期:2014-07-29 接受日期:2014-07-29 出版日期:2014-07-29 发布日期:2014-07-29

MacWilliams identities of linear codes over Mn×s(Rk) with respect to RT metric

YAO Ting, SHI Minjia, LIU Yan

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

Received:2014-06-05 Revised:2014-07-29 Accepted:2014-07-29 Online:2014-07-29 Published:2014-07-29
Contact: SHI Minjia
About author:YAO Ting, female, born in 1989, master candidate. Research field: Algebraic codingtheory. E-mail: yaoting_1649@163.com
Supported by:
Supported by NNSF of China (61202068), Talents youth Fund of Anhui Province Universities (2012SQRL020ZD).

摘要/Abstract

摘要： 定义了环Mn×s(Rk)(u2i=0,uiuj=ujui)上线性码的Lee完全ρ重量计数器和精确完全ρ重量计数器,并给出了环Mn×s(Rk)上线性码关于这两种重量计数器的MacWilliams恒等式.最后给出两个例子对所得的结果进行了验证.

关键词: RT距离, 重量计数器, MacWilliams恒等式, 对偶码

Abstract: The definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator over Mn×s(Rk)(u2i=0,uiuj=ujui) were given, and the MacWilliams identities with respect to the RT metric for these two weight enumerators of linear codes over Mn×s(Rk) were obtained, respectively. Finally, two examples were presented to illustrate our obtained results.

Key words: RT metric, weight enumerator, MacWilliams identity, dual code

中图分类号:

TN911.22

姚婷，施敏加，刘艳. 环Mn×s(Rk)上线性码关于RT距离的MacWilliams恒等式[J]. 中国科学技术大学学报, 2015, 45(1): 34-39.

YAO Ting, SHI Minjia, LIU Yan. MacWilliams identities of linear codes over Mn×s(Rk) with respect to RT metric[J]. Journal of University of Science and Technology of China, 2015, 45(1): 34-39.

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环Mn×s(Rk)上线性码关于RT距离的MacWilliams恒等式

MacWilliams identities of linear codes over Mn×s(Rk) with respect to RT metric

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