摘要
C is an [n, k, d]q linear code over Fq. And s（C） = n ＋ 1 - k - d is the Singleton defect of C. An MDS 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.
基金
supported by Key Disciplines of Shanghai Municipality under Grant No.S30104
