Families of weighing matrices

Abstract

A weighing matrix is an n × n matrix W = W(n, k) with entries from {0, 1, −1}, 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 × 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 ≤ t.