环R+vR+v^2R上线性码的MacWilliams恒等式  

MacWilliams Identities of Linear Codes Over Ring R+vR+v^2R

作　　者：朱士信[1] 黄磊[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《电子学报》2016年第7期1567-1573,共7页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61370089)

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Mac Williams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.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.

关 键 词：线性码 GRAY映射 对偶码 重量计数器 MACWILLIAMS恒等式 

分 类 号：TN911.22[电子电信—通信与信息系统]