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. For odd prime power $q$ with $q$ square, the total number of lengths for MDS self-dual codes over $mathbb{F}_q$ presented in this paper is much more than those in all the previous results.
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