A Family of Balanced Generalized Weighing Matrices

Balanced weighing matrices with parameters (1 + 18 ·9^m + 1 - 1 8,9^m + 1,4 ·9^m), for each nonzero integer m are constructed. This is the first infinite class not belonging to those with classical parameters. It is shown that any balanced weighing matrix is equivalent to a five-class association scheme.