A family of balanced generalized weighing matrices

Abstract

Balanced weighing matrices with parameters $$\left(1+18\cdot \frac{9^{m+1}-1}{8},9^{m+1},4\cdot 9^m\right),$$ for each nonzero integer $m$ is 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.

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