A Family of Balanced Generalized Weighing Matrices

Abstract

Balanced weighing matrices with parameters

$$\left({1 + 18 \cdot {{{9^{m + 1}} - 1} \over 8},{9^{m + 1}},4 \cdot {9^m}} \right),$$

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.