一类Z_p上的非线性码  

A Family of Nonlinear Codes over Z_p

作　　者：董久祥[1] 董学东[2] 张妍[2] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004 [2]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2006年第2期129-132,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10171042)

摘　　要：Asch等人将Gray映射推广为Zp2到Zp的等距映射并构造了两类Zp上的非线性码,其中p为奇素数.笔者进一步将Gray映射推广并将Zps(s≥2)上的一类线性码映射为Zp上的一类具有较大距离的非线性码,其中p为奇素数.A relation was established between linear codes over Z4 and certain interesting non-linear binary codes of even length by means of the so called Gray map. Asch et al. generalized the Gray map to an isometry between Zp^2 and Zp and constructed two ＂dual＂ families of nearly-linearly codes over Zp, where p is an odd prime. We further generalize the Gray map and get a family of non-linear codes over Zp,where p is an odd prime. These codes have large distances.

关 键 词：GRAY映射 GALOIS环 非线性码 基本不可约多项式 

分 类 号：O236.2[理学—运筹学与控制论]