I. Introduction
MDS codes and Euclidean self-dual codes belong to two different categories of block codes. Both classes are of practical and theoretical importance. In recent years, study of Maximum Distance Separable (MDS for short) self-dual codes (we only consider Euclidean inner product in the following context) has attracted a lot of attention [1]–[3], [9]–[14]. First of all, MDS codes achieve optimal parameters that allow correction of maximal number of errors for a given code rate. Study of various properties of MDS codes, such as classification [15], [20] of MDS codes, non-Reed-Solomon MDS codes [21], balanced MDS codes [6], lowest density MDS codes [4], [17] and existence of MDS codes [7], has been the center of the area. In addition, MDS codes are closely connected to combinatorial design and finite geometry [18, Ch. 11 and 14]. Furthermore, the generalized Reed-Solomon codes are a class of MDS codes and have found wide applications in practice. On the other hand, due to their nice structures, self-dual codes have been attracting attention from both coding theorists, cryptographers and mathematicians. Self-dual codes have found various applications in cryptography (in particular secret sharing) [5], [8], [19] and combinatorics [18]. Thus, it is natural to consider the intersection of these two classes, namely, MDS self-dual codes.