Almost Orthogonal MDS Matrices over GR(2n, k)

MDS matrices are excellent candidate for providing diffusion properties in block ciphers. While MDS matrices over F_2(k) are more commonly used, the paper [12] suggested to consider the use of MDS matrices over Galois ring GR(2ⁿ, k). In this paper, we explore some constructions of MDS matrices over GR(2ⁿ, k) with special properties (e.g, Hadamard, almost orthogonal) from given MDS matrices over F_2(k). We show that 2^r × 2^r enabling Hadamard (1, -1) -matrices do not exist for r ≥ 4. We also give an algorithm to construct almost orthogonal MDS matrices over GR(2ⁿ, k).