On inequivalent weighing matrices

Abstract

A weighing matrix W = W(n,k) of order n and weight k is a square matrix of order n, with entries 0, +1 aud -1 which satisfies WWT = kIn. Tools such as Smith Normal Form, profile, maximum integer and some group theoretic and coding theory methods are used to classify some matrices for 1 ≤ k ≤ n ≤ 20, into equivalence classes under pre-and post-multiplication by monomial matrices(permutation matrices where the non-zero elements are +1 or -1). The inequivalent weighing matrices are classified for k ≤ 5.