| 环Fp+vFp+v2Fp上线性码的各种重量计数器及其MacWilliams恒等式 |
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| 引用本文： | 施敏加,刘艳.环Fp+vFp+v2Fp上线性码的各种重量计数器及其MacWilliams恒等式[J].电子学报,2014,42(7):1387-1391. |
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| 作者姓名： | 施敏加 刘艳 |
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| 作者单位： | 安徽大学数学科学学院, 安徽合肥 230601 |
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| 基金项目： | 国家自然科学基金(No ．61202068)；安徽省高校优秀青年人才基金重点项目 |
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| 摘 要： | 首先给出了环R=Fp+vFp+v2Fp上线性码及其对偶码的结构及其Gray象的性质.定义了环R上线性码的各种重量计数器并讨论了它们之间的关系，特别的，确定了该环上线性码与其对偶码之间关于完全重量计数器的MacWilliams恒等式，利用该恒等式，进一步建立了该环上线性码与其对偶码之间的一种对称形式的MacWilliams恒等式.最后，利用该对称形式的MacWilliams恒等式得到了该环上的Hamming重量计数器和Lee重量计数器的MacWilliams恒等式，利用不同的方法推广了文献7]中的结果.
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| 关 键 词： | 线性码 完全重量计数器 对称重量计数器 MacWilliams恒等式 |
| 收稿时间： | 2013-10-22 |
Several Weight Enumerators of Linear Codes and Their MacWilliams Identities over Ring Fp + vFp + v2 Fp |
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| SHI Min-jia,LIU Yan.Several Weight Enumerators of Linear Codes and Their MacWilliams Identities over Ring Fp + vFp + v2 Fp[J].Acta Electronica Sinica,2014,42(7):1387-1391. |
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| Authors: | SHI Min-jia LIU Yan |
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| Affiliation: | School of Mathematical Sciences of Anhui University, Hefei, Anhui 230601, China |
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| Abstract: | We first give the structures of linear codes and the proposition of their Gray images.A complete weight enumerator of linear codes over ring R=Fp+vFp+v2Fp is defined;we define some weight enumerators of linear codes and their dual codes,and then discuss the relations between them.A MacWilliams identity between linear codes and their dual over R with respect to the complete weight enumerator is given.By using this identity,a symmetrized form MacWilliams identitiy between linear codes and their dual over the ring is also established,and MacWilliams identities with respect to Hamming and Lee enumerator can be as results of the symmetrized MacWilliams identitiy,we generalize the results in7] using different method. |
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| Keywords: | linear code complete weight enumerator symmetrized weight enumerator MacWilliams identity |
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