Balanced weighing matrices

A weighing matrix of order n and weight p, denoted W (n, p), is a (0,±1)matrix W of order n such that WW t = pIn. The special cases in which n = p + 1 is called a conference matrix and n = p is a Hadamard matrix. A weighing matrix W (n, p) is said to be balanced if, upon setting each nonzero entry to unity, it provides the incidence matrix of a symmetric (n, p, λ) balanced incomplete block design.