MDS self-dual codes

In this paper we develop a complete generalization of the building-up method [J.-L. Kim, (2001)] for the Euclidean and Hermitian self-dual codes over finite fields GF(q). Using this method we construct many new Euclidean and Hermitian self-dual MDS (or near MDS) codes of length up to 12 over various finite fields GF(q), where q=8, 9, 16, 25, 32, 41, 49, 53, 64, 81, and 128.