On the Smith normal form of weighing matrices

The Smith normal forms (SNF) of weighing matrices are studied. We show that for all orders n ≥ 35 the full spectrum of Smith normal forms (SNF) exists for weighing matrices W(n,9) ie there exists a W(n,9) with SNF 11/2(n-s)3s91/2(n-s), for s in a set, which is described, of consecutive integers.