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A two-parameter family of $2$-$(4n^2,n(2n-1),m(n-1))$ designs are
constructed starting from a certain block matrix with $2n$ by $2m$
sub-matrices, and a balanced generalized weighing matrix over an
appropriate cyclic group. The special case $n=m$ corresponds to a
construction of symmetric 2-designs from Hadamard matrices of Bush
type described in [10]. If $2m$ and $2n$ are the orders of
Hadamard matrices, the construction yields Hadamard matrices of
Bush type. Furthermore, if either $2n-1$ or $2n+1$ is a prime
power, the designs can be expanded to infinitely many new designs
by using known balanced generalized weighing matrices.
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