一种有限域上自正交码的构造方法  

A Method for Constructing Self-orthogonal Codes Over Finite Fields

作　　者：张付丽[1] 开晓山[1] 朱士信[1] 陈安顺[2] 

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]滁州学院数学科学学院.滁州239000

出　　处：《电子与信息学报》2014年第10期2326-2330,共5页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(61370089);安徽省自然科学基金(1208085MA14,1408085QF116);安徽省高等学校省级优秀青年人才基金(2012SQRL156);滁州学院校级科研项目(2011kj002B)资助课题

摘　　要：该文利用有限环q qF+uF上循环自正交码,给出了一种构造有限域qF上自正交码的方法。引入了q qF+uF到pqF的等距Gray映射,给出了q qF+uF上循环自正交码存在的充分必要条件,证明了q qF+uF上长为n的循环自正交码的Gray象是qF上长为pn的自正交码,由此构造了qF上一些参数较好的自正交码。A method is proposed to construct self-orthogonal codes over the finite field Fq by using cyclic self-orthogonal codes over the finite ring q qF ？uF . A Gray map from q qF ？uF to pqF is introduced, and a sufficient and necessary condition for the existence of cyclic self-orthogonal codes over q qF ？uF is given. It is proved that the Gray image of a cyclic self-orthogonal code with length n over q qF ？uF is a self-orthogonal code with length pn over Fq . Further, some self-orthogonal codes over Fq with good parameters are constructed.

关 键 词：循环码 GRAY映射 自正交码 

分 类 号：TN911.22[电子电信—通信与信息系统]