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Orthogonal matrices with indeterminate
entries are called orthogonal designs. There is a strong relationship between orthogonal designs and quadratic forms. Orthogonal designs are used to construct Hadamard matrices and, more generally, weighing
matrices. Despite the importance of orthogonal designs, not much is known about their existence or construction. We use a powerful new constructive technique to find a kind of asymptotic existence result
for orthogonal designs.
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