PDF(281 KB)
PDF(281 KB)
PDF(281 KB)
环Z4+uZ4线性码关于李重量的一类MacWilliams恒等式
A Type of MacWilliams Identity for Linear Codes over Z4+uZ4 on Lee Weight
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.
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.
线性码 / 李重量 / m-层重量计数器 / MacWilliams恒等式 {{custom_keyword}} /
linear codes / Lee weight / m-ply weight enumerator / MacWilliams identities {{custom_keyword}} /
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国家自然科学基金 (No.61370089); 安徽省自然科学基金 (No.1408085QF116); 安徽省高校省级科学研究项目 (No.KJ2013B221); 合肥工业大学博士专项科研资助基金 (No.JZ2014HGBZ0029); 中央高校基本科研业务费专项资金资助项目 (No.J2014HGXJ0073); 东南大学移动通信国家重点实验室开放研究基金资助课题 (2014D04); 2014年安徽省高校优秀青年人才支撑计划项目 (No.皖教秘人[2014]181); 合肥师范学院校级科研机构基金 (No.2015JG09)
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