Quasi-balanced weighing matrices, signed strongly regular graphs and association schemes

Hadi Kharaghani, Thomas Pender, Sho Suda

A weighing matrix $W$ is quasi-balanced if $|W||W{|}^{\top }=|W{|}^{\top }|W|$ has at most two off-diagonal entries, where $|W{|}_{ij}=|W_{ij}|$. A quasi-balanced weighing matrix $W$ signs a s…