On m-MDS codes over finite fields

摘要

Let C~⊥ be the dual code of the q-ary linear code C = [n,k,d]_q and S(C) =n+1-k-d = m(≥ 0) be the Singleton defect of C. Several sufficient and necessary conditions for that C = [n, k, d]_q satisfies S(C) = S(C~⊥) = m are obtained. Furthermore, all q-axy Hamming m-MDS codes are determined.