环Z_4上自对偶码的构造  

A Method for Construction Self-dual Codes over Z_4

作　　者：袁健[1,2] 朱士信[1,2] 开晓山[1,2] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009 [2]东南大学移动通信国家重点实验室,江苏南京210096

出　　处：《电子学报》2016年第11期2807-2811,共5页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61370089);东南大学移动通信国家重点实验室开放研究基金(No.2014D04);安徽省自然科学基金(No.JZ2015AKZR0021;No.1508085SQA198)

摘　　要：利用有限环Z_4+v Z_4(其中v_2=1)上自对偶码,给出了一种构造Z_4上自对偶码的方法.引入了(Z_4+v Z_4)n到Z_2n_4的保距Gray映射,给出了Z_4+v Z_4上自对偶码的性质,证明了Z_4+v Z_4上长为n的自对偶码的Gray像是Z_4上长为_2n的自对偶码,由此构造了Z_4上一些极优的类型I与类型Ⅱ自对偶码.A Method for Construction self-dual codes over Z4 is proposed by using self-dual codes over the ring Z4 ＋ vZ4 ,where v2 = 1. A Gray map from （Z4 ＋vZ4）n to Z2n is introduced,and some properties about self-dual codes over Z4 ＋ vZ4 are given. It showns that the Gray image of a self-dual code over Z4 ＋ vZ4 of length n is a self-dual code over Z4 of length 2n. Further, some extremal Type I and Type II codes over Z4 are constructed.

关 键 词：GRAY映射 线性码 自对偶码 

分 类 号：TN991.22[电子电信—信号与信息处理]