Families of weighing matrices

Abstract

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