| 环R+vR+v2R上线性码的MacWilliams恒等式 |
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| 引用本文： | 朱士信,黄磊.环R+vR+v2R上线性码的MacWilliams恒等式[J].电子学报,2016,44(7):1567-1573. |
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| 作者姓名： | 朱士信 黄磊 |
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| 作者单位： | 合肥工业大学数学学院, 安徽合肥 230009 |
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| 基金项目： | 国家自然科学基金(61370089) |
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| 摘 要： | 通过构造Gray映射,对环R+vR+v2R上线性码进行了研究.定义了环R+vR+v2R上线性码的Lee重量及其几类重量计数器,给出了环R+vR+v2R上线性码及其对偶码之间的各种重量分布的MacWilliams恒等式.利用这些恒等式,不用求出环R+vR+v2R上线性码的对偶码便可得到对偶码的各种重量分布.
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| 关 键 词： | 线性码 Gray映射 对偶码 重量计数器 MacWilliams恒等式 |
| 收稿时间： | 2014-12-26 |
MacWillia ms Identities of Linear Codes Over Ring R+vR+v2R |
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| ZHU Shi-xin,HUANG Lei.MacWillia ms Identities of Linear Codes Over Ring R+vR+v2R[J].Acta Electronica Sinica,2016,44(7):1567-1573. |
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| Authors: | ZHU Shi-xin HUANG Lei |
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| Affiliation: | School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China |
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| Abstract: | By constructing gray map,linear codes over ring R+vR+v2 R are studied.The Lee weight and several clas-ses of weight enumerators about linear codes over ring R+vR+v2 R are defined,the MacWilliams identities of weight distri-butions between the linear codes and their dual codes over ring R+vR+v2 R are given.According to these identities,we can get the weight distributions of dual codes directly without obtaining the dual codes of linear codes over ring R+vR+v2 R. |
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| Keywords: | linear code Gray map dual code weight enumerator MacWilliams identity |
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