On l-th NMDS Codes  

作　　者：TONG Hongxi CHEN Wenhai YU Fei 

机构地区：[1]Department of Mathematics,Shanghai University [2]Science and Technology on Communication Security Laboratory

出　　处：《Chinese Journal of Electronics》2014年第3期454-457,共4页电子学报（英文版）

摘　　要：Linear codes with Singleton defects equivalent to 0, 1, 2 are studied, and they have good properties. They are called MDS codes, NMDS codes, NNMDS cdoes, respectively. In this paper, we study linear codes with large Singleton defects and these codes have same good properties with MDS codes, NMDS codes, NNMDS codes. We call them l-th NNIDS codes. A series of iff con- ditions of l-th NMDS codes is presented. And we give an upper bound on length of l-th NMDS codes. In the last, some examples of l-th NMDS codes are given.Linear codes with Singleton defects equivalent to 0, 1, 2 are studied, and they have good properties. They are called MDS codes, NMDS codes, NNMDS cdoes, respectively. In this paper, we study linear codes with large Singleton defects and these codes have same good properties with MDS codes, NMDS codes, NNMDS codes. We call them l-th NMDS codes. A series of iff conditions of l-th NMDS codes is presented. And we give an upper bound on length of l-th NMDS codes. In the last,some examples of l-th NMDS codes are given.

关 键 词：Linear codes Maximum distance separated （MDS） codes Singleton defects Near maximum distance separated （NMDS） codes Generalized Hamming weights. 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]