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Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
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On the half-skew-centrosymmetric Hadamard matrices
Let $H_n$ be an $n×n$ Hadamard matrix and $R_n$ the $n×n$ reverse identity matrix.
The matrix $X= \begin{pmatrix}
H_n & R_nH_n \\
H_n & -R_nH_n
\end{pmatrix}$ has entries of length $1$ and $$XX^* = 2n …