Abstract
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 degree
Publication Details
A.V. Geramita, N.J. Pullman and Jennifer Seberry Wallis, Families of weighing matrices, Bulletin of the Australian Mathematical Society, 10, (1974), 119-122.