$k$-configurations

An overview of classification theorems and methods for constructing $k$-configurations defined by their incident matrices $L$ is given. They are nondegenerate over the field $GF(2)$. Each row and each column of the matrices $L,\,L^{-1}$ contains exactly $k$ units. To construct $k$-configurations, we use regular polyhedra, regular and symmetric graphs, quadratic residues and nonquadratic residues of finite fields, finite groups, $(v,k,\lambda)$-configurations, including perfect difference sets, finite projective planes, and Hadamard matrices.