I am facing matrices in which every entry is $\pm 1$ and every row and column sums to the same constant, e.g.,
$$M=\begin{pmatrix} 1 & -1 & -1 & 1 & -1\\ -1 & -1 & -1 & 1 & 1\\ -1 & 1 & 1 & -1 & -1\\ 1 & 1 & -1 & -1 & -1\\ -1 & -1 & 1 & -1 & 1\end{pmatrix}.$$
They are closely related to $(0, 1)$-matrices with the same property, as $\frac{1}{2}M+J$ results in such a matrix. Are there some references/theory/research/results on such matrices?