%0 Journal Article %T Equivalence of the Existence of Hadamard Matrices and Cretan$(4t-1,2)$-Mersenne Matrices %A Jennifer Seberry %A N. A. Balonin %J Mathematics %D 2015 %I arXiv %X We study orthogonal matrices whose elements have moduli $\leq 1$. This paper shows that the existence of two such families of matrices is equivalent. Specifically we show that the existence of an Hadamard matrix of order $4t$ is equivalent to the existence of a Cretan$(4t-1,2)$-Mersenne matrix. %U http://arxiv.org/abs/1501.07012v1