| 环Z4+uZ4线性码关于李重量的一类MacWilliams恒等式 |
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| 引用本文： | 李平,李珊珊,唐永生.环Z4+uZ4线性码关于李重量的一类MacWilliams恒等式[J].电子学报,2015,43(12):2461-2465. |
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| 作者姓名： | 李平 李珊珊 唐永生 |
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| 作者单位： | 1. 合肥工业大学数学学院, 安徽合肥 230009;
2. 合肥师范学院数学与统计学院, 安徽合肥 230601 |
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| 摘 要： | MacWilliams恒等式是研究线性码及其对偶码的码字重量分布的一个非常有用的工具,而码字的重量分布的研究是编码研究中一个非常重要的研究方向.本文定义了环Z4+uZ4上长度为n的线性码的m-层李重量计数器,给出了环Z4+uZ4上长度为n的线性码关于李重量的一类MacWilliams恒等式.证明了该等式是生成矩阵在环Z4+uZ4上的环GR(4,m)+uGR(4,m)上线性码关于李重量的MacWilliams恒等式.进一步,利用Krawtchouk多项式,获得了环Z4+uZ4上长度为n的线性码的等价形式MacWilliams恒等式.
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| 关 键 词： | 线性码 李重量 m-层重量计数器 MacWilliams恒等式 |
| 收稿时间： | 2014-05-06 |
A Type of MacWilliams Identity for Linear Codes over Z4+uZ4 on Lee Weight |
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| LI Ping,LI Shan-shan,TANG Yong-sheng.A Type of MacWilliams Identity for Linear Codes over Z4+uZ4 on Lee Weight[J].Acta Electronica Sinica,2015,43(12):2461-2465. |
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| Authors: | LI Ping LI Shan-shan TANG Yong-sheng |
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| Affiliation: | 1. School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China;
2. School of Mathematics and Statistics, Hefei Normal University, Hefei, Anhui 230601, China |
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| Abstract: | MacWilliams identity is an useful tool in studying weight distributions of linear codes and their duals.Weight distribution is also an important topic of coding theory.This paper defines the m-ply Lee weight enumerators for linear codes of length n over Z4+u Z4.We give a type of Mac-Williams identity for linear codes of length n over Z4+u Z4 on Lee weight.We prove that this identity is the MacWilliams identity on Lee weight for linear codes over GR(4,m)+uGR(4,m)having generator matrix over Z4+u Z4.Furthermore,by means of Krawtchouk polynomials the equivalent form of the type of MacWilliams identity for linear codes of length n over Z4+u Z4 is obtained. |
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| Keywords: | linear codes Lee weight m-ply weight enumerator MacWilliams identities |
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