NNMDS codes

C is an n, k, d] _q linear code over $\mathbb{F}_q $ . And s(C) = n + 1 ? k ? d is the Singleton defect of C. AnMDS code C with s(C) = 0 has been studied extensively. Recently, a near-MDS code C with s(C) = s(C ^??) = 1 is studied by many scholars, where C ^?? denotes the dual code of C. This paper concentrates on the linear code C with s(C) = s(C ^??) = 2, and the author calls it an NNMDS code. A series of iff conditions of NNMDS codes are presented. And the author gives an upper bound on length of NNMDS codes. In the last, some examples of NNMDS are given.