NMDS codes of maximal length over [F.sub.q], 8 [less than or equal to] q [less than or equal to] 11

A linear [[n, k, d].sub.q] code C is called near maximum-distance separable (NMDS) if d(C) = n - k and d([C.sup.[perpendicular to]]) = k. The maximum length of an NMDS [[n, k, d].sup.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 [less than or equal to] m'(4, 11) [less than or equal to] 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. Index Terms--Galois fields, linear codes, near maximum-distance separable (NMDS) codes.