Publication Details

Jennifer Seberry Wallis, Some matrices of Williamson type, Utilitas Mathematica, 4, (1973), 147-154.


Recent advances in the construction of Hadamard matrices have depended on the existence of Baumert-Hall arrays and four (1,-1) matrices A, B, C, D of order m which are of Williamson type; that is, they pairwise satisfy

(i) MNT = NMT, and

(ii) AAT + BBT + CCT + DDT = 4mIm

We show that if p = 1 (mod 4) is a prime power then such matrices exist for m = 1/2p(p+1). The matrices constructed are not circulant and need not be symmetric. This means there are Hadamard matrices of order 2p(P+1)t and 10p(p+1)t for t E {1,3,5,...,59} u {1 + 2a 10b26c ,a,b,c non-negative integers} , which is a new infinite family.