环F_(q)F_(q)[u,v]上加性码的MacWilliams恒等式  

MacWilliams identities of additive codes over the ring F_(q)F_(q)[u,v]

作　　者：李冰 吴化璋[1] LI Bing;WU Huazhang(School of Mathematical Sciences,Anhui University,Hefei Anhui 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《阜阳师范大学学报（自然科学版）》2022年第1期11-16,共6页Journal of Fuyang Normal University:Natural Science

基　　金：教育部信号过程与智能计算重点实验室2017年重点开放课题(信号处理与代数编码中的矩阵计算)。

摘　　要：定义了一类环F_(q)F_(q)[u,v]上的加性码,其中q是素数的方幂,分别讨论了该环上加性码的Lee重量,Hamming重量和对称重量计数器。并利用Gray映射,给出该环上加性码与其对偶码之间关于Lee重量的MacWilliams恒等式。最后给出一个例子说明该恒等式。In this paper a class of F_(q)F_(q)[u,v]-additive codes was introduced,where q was a power of a prime.The Lee weight,the Hamming weight and the symmetrical weight enumerators of additive codes over the ring F_(q)F_(q)[u,v]were discussed,respectively.Moreover,using the Gray mapping,the MacWilliams identities between an additive code and its dual code on the Lee weight were discussed.Finally,an example was given to illustrate the above identities.

关 键 词：加性码 GRAY映射 Lee重量 MACWILLIAMS恒等式 

分 类 号：O157.4[理学—数学]