On l-th NMDS Codes

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.