Notes on MDS self-dual codes (Q2919914)

Self-dual codes and MDS codes have been an active research area in coding theory. The author considers a class of MDS self-dual codes over \(\mathbb F_q\). The paper is motivated by the results on the existence of MDS self-dual codes in [\textit{M. Grassl} and \textit{T. A. Gulliver}, ``On self-dual MDS codes'', in: Proceedings of the IEEE international symposium on information theory, Toronto, Canada, 2008. Los Alamitos: IEEE. 1954--1957 (2008)]. They showed that for \(q = 2^m,\) there are MDS self-dual codes for all even lengths up to \(2^m\). They also showed that MDS self-dual codes of length \(q + 1\) over \(\mathbb F_q\) exist for all odd prime powers \(q\). The author proves that for all odd prime powers \(q\), there exist MDS self-dual codes over \(\mathbb F_{q^2}\) for all even lengths up to \(q + 1\).