On self-dual MDS codes

We consider the problem for which lengths a self-dual MDS code over F<sub>q</sub> exists.We show that for q = 2<sup>m</sup>, there are self-dual MDS codes for all even lengths up to 2<sup>m</sup>. Furthermore, self-dual MDS codes of length q + 1 over F<sub>q</sub> exist for all odd prime powers q. Additionally, we present some new self-dual MDS codes.

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