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 Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_q$$\end{document} presented in this paper is much more than those in all the previous results.