On good matrices and skew hadamard matrices

Abstract

In her Ph.D. thesis (Seberry)Wallis described a method using a variation of the Williamson array to find suitable matrices, which we will call good matrices, to construct skew Hadamard matrices. Good matrices were designed to plug into the Seberry-Williamson array to give skew-Hadamard matrices. We investigate the properties of good matrices in an effort to find a new, efficient, method to compute these matrices. We give the parameters of the supplementary difference sets (SDS) which give good matrices for use in the Seberry-Williamson array.