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Regular Hadamard matrices constructed from Hadamard 2-designs and conference graphs

Suppose there exists a Hadamard 2-$(m, (m−1)/2, (m−3)/4)$ design having skew incidence matrix. If there exists a conference graph on $2m−1$ vertices, then there exists a regular Hadamard matrix of order $4m^2$. A conference graph on $2m+3$ vertices yields a regular Hadamard matrix of order $4(m+1)^2$.

Regular Hadamard matrix ; Hadamard 2-design ; Conference graph

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