A construction of MDS involutory matrices using MDS self-dual codes: a preliminary result

The Maximum Distance Separable (MDS) matrices have an important application in cryptography, for example see [1]. In order to reduce the implementation complexities, it is important to consider MDS matrices which are involutory. Some constructions of involutory MDS matrices can be found in [2, 3]. In this paper, we give some properties related to a construction of involutory MDS matrices using orthogonal matrices derived from Euclidean self-dual MDS codes. Then, we do a computer search to find involutory MDS matrices with small sizes using classical simulated annealing algorithm. The proposed construction is different compared to the ones in [2, 3].