New MDS or near-MDS self-dual codes

We construct new MDS or near-MDS self-dual codes over large finite fields. In particular, we show that there exists a Euclidean self-dual MDS code of length n = q over GF(q) whenever q = 2(m) (m >= 2) using a Reed-Solomon (RS) code and its extension. It turns out that this multiple description source (MDS) self-dual code is an extended duadic code. We construct Euclidean self-dual near-MDS codes of length n = q-1 over GF(q) from RS codes when q equivalent to 1 (mod 4) and q <= 113. We also construct many new MDS self-dual codes over GF(p) of length 16 for primes 29 <= p <= 113. Finally, we construct Euclidean/Hermitian self-dual MDS codes of lengths up to 14 over GF(q(2)) where q = 19,23,25,27,29.