New MDS Self-dual Codes over Finite Fields of Odd Characteristic

In this paper, we produce new classes of MDS self-dual codes via (extended) generalized Reed–Solomon codes over finite fields of odd characteristic. Among our constructions, there are many MDS self-dual codes with new parameters which have never been reported. When q is square of odd prime power, the total number of lengths of MDS self-dual codes over $$\mathbb {F}_q$$ presented in this paper is much more than those in all the previous results.