Families of weighing matrices

Families of weighing matrices A weighing matrix is an n x n matrix W = W(n, k) with entries from {0, 1,-l}, satisfying WWt = kIn. We shall call k the degree of W. It has been conjectured that if n = 0 (mod 4) then there exist n x n weighing matrices of every degree k < n. We prove the conjecture when n is a power of 2. If n is not a power of two we find an integer t < n for which there are weighing matrices of every degre