Abstract
In this paper, we consider the problem for which lengths a maximum distance separable (MDS) Euclidean self-dual code over $\mathbb {F}_{q}$ exists. This problem is completely solved for the case where $q$ is even. For $q$ is odd, some $q$ -ary MDS Euclidean self-dual codes were obtained in the literature. In this paper, we construct six new classes of $q$ -ary MDS Euclidean self-dual codes by using generalized Reed–Solomon (GRS for short) codes and extended GRS codes.
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