Symmetric Conference Matrices of Order pq 2 + 1

Abstract

A conference matrix of order n is a square matrix C with zeros on the diagonal and ±1 elsewhere, which satisfies the orthogonality condition CC T = (n — 1)I. If in addition C is symmetric, C = C T , then its order n is congruent to 2 modulo 4 (see [ 5 ]). Symmetric conference matrices ( C ) are related to several important combinatorial configurations such as regular two-graphs, equiangular lines, Hadamard matrices and balanced incomplete block designs [ 1 ; 5 ; and 7, pp. 293-400]. We shall require several definitions.