Discovery of an Hadamard matrix of order 92

Abstract

An Hadamard matrix H is an n by n matrix all of whose entries are +1 or -1 which satisfies HH T = n J, H T being the transpose of H. The order n is necessarily 1, 2 or 42, with t a positive integer. R. E. A. C. Paley [3] gave construction methods for various infinite classes of Hadamard matrices, chiefly using properties of quadratic residues in finite fields. These constructions cover all values of 4^200, except 4/ = 92, 116, 156, 172, 184, 188. Further constructions have been given by J. Williamson [5; 6], A. Brauer [l], M. Hall [2] and R. Stanton and D. Sprott [4]. Williamson's first paper gave an Hadamard matrix of order 172, incorporating a special automorphism of order 3. The same method may be applied to 92, 116, 156, and 188, but Williamson did not do so, principally because of the amount of computation involved.