环Z_4+vZ_4上的线性码:重量计数器及其Macwilliams恒等式  

LINEAR CODES OVER RING Z_4+vZ_4:WEIGHT ENUMERATORS AND THEIR MACWILLIAMS IDENTITIES

作　　者：刘丽[1] 王艳[1] 

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《系统科学与数学》2014年第8期1003-1013,共11页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11071186;11201107);安徽省自然科学基金(1208085QA01)资助项目

摘　　要：首先给出了环R=Z_4+vZ_4(v^2=v)上线性码的Gray映射及其投影映射的性质,得到了环R上线性码与通过投影映射得到的线性码的极小Lee重量的关系,然后定义了环R上线性码的Gray重量计数器和对称重量计数器,进一步地确定了环R上线性码与其对偶码之间关于Gray重量计数器,对称重量计数器和Lee重量计数器的MacWilliams恒等式.In this paper, first we give the propositions of Gray maps and several projections of linear codes over the ring R = Za ＋ vZ4（v2 = v） and consider the relationship of minimum Lee weight between the linear codes over the ring R and the corresponding codes which are obtained by means of the projections. Next, by defining the Gray weight enumerator and symmetrized weight enumerator, we could establish the MacWilliams identities between linear codes and their dual over the ring R with respect to the Gray weight enumerator, the symmetrized weight enumerator and the Lee weight enumerator.

关 键 词：线性码 投影映射 Gray重量计数器 对称重量计数器 MacWilliams恒等式. 

分 类 号：O157.4[理学—数学]