Some new orders of Hadamard and skew-Hadamard matrices

Abstract

We construct Hadamard matrices of orders 4x251 = 1004 and 4x631 = 2524, and skew-Hadamard matrices of orders 4x213 = 852 and 4x631 = 2524. As far as we know, such matrices have not been constructed previously. The constructions use the Goethals-Seidel array, suitable supplementary difference sets on a cyclic group and a new efficient matching algorithm based on hashing techniques.