A Skew Hadamard Matrix of Order 52

Abstract

1. A Hadamard (H-) matrix H = (hij) of order n is an n × n square matrix satisfying the conditionsfor all i, j ≦ n. A skew H-matrix is an H-matrix of the formwhere I is the identity matrix and S’ the transpose of 5. In particular,Skew H-matrices have applications in the theory of finite projective planes (2) and tournaments (4), also in the construction of H-matrices of certain orders. For example, if there is a skew H-matrix of order n, then there is an H-matrix of order n(n – 1) (Williamson, see (1, p. 213)).