NMDS codes of maximal length over Fq,8⩽q⩽11

A linear [n,k,d]_q code C is called near maximum-distance separable (NMDS) if d(C)=n-k and d(C^⊥)=k. The maximum length of an NMDS [n,k,d]_q code is denoted by m´(k,q). In this correspondence, it has been verified by a computer-based proof that m´(5,8)=15, m´(4,9)=16,m´(5,9)=16, and 20⩽m´(4,11)⩽21. Moreover, the NMDS codes of length m´(4,8), m´(5,8), and m´(4,9) have been classified. As the dual code of an NMDS code is NMDS, the values of m´(k,8), k=10,11,12, and of m´(k,9),k=12,13,14 have been also deduced