New Constructions of MDS Euclidean Self-Dual Codes From GRS Codes and Extended GRS Codes

In this paper, we consider the problem for which lengths a maximum distance separable (MDS) Euclidean self-dual code over Fq 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.