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. [ABSTRACT FROM AUTHOR]