有限主理想环上接近MDR码  

Near-MDR codes over finite principal ideal rings

作　　者：张晓燕[1] 

机构地区：[1]湖北理工学院数理学院,湖北黄石435003

出　　处：《山东大学学报（理学版）》2015年第6期59-63,共5页Journal of Shandong University(Natural Science)

基　　金：湖北省教育厅自然科学基金重点项目(D20144401)

摘　　要：将有限域上接近MDS码的概念推广到有限主理想环上的接近MDR码。利用有限主理想环上线性码为有限链环上线性码的中国积,将有限主理想环上线性码为接近MDR码的判定转化成有限链环上接近MDR码的判定。进一步,将有限链环上接近MDR码的判定转化为它的剩余类域上接近MDS码的判定,从而描述了有限主理想环上接近MDR码。The definition of Near-MDS codes over finite fields was generalized to near-MDR codes over finite principal ideal rings. Using the fact that a linear codes over a finite principal ideal ring is the Chinese product of the linear codes over finite chain rings, the criterion of near-MDR codes over finite principal ideal rings are changed into that of near- MDR codes over finite chain rings. Furthermore, the criterion of near-MDR codes over finite chain rings is changed into that of near-MDS codes over residue fields, so we describe near-MDR codes over finite principal ideal rings.

关 键 词：有限主理想环 有限链环 几乎MDR码 接近MDR码 

分 类 号：TN911.22[电子电信—通信与信息系统]