Power Hadamard matrices (Q924977)

Generalizations of Hadamard matrices are surveyed, and yet another generalization is introduced, power Hadamard matrices, which overlaps the other generalizations discussed in the paper. A power Hadamard matrix is an \(n \times n\) matrix \(H\) with entries that are integer powers of \(x\) and that satisfies \(HH^* = nI\) modulo \(f(x)\), where \(f\) is some Laurent polynomial of degree greater than \(0\) (\(H^*\) is the Hermitian adjoint of \(H\) and \(I\) is the identity matrix). The basic theory of power Hadamard matrices is developed, and the paper is concluded with many interesting open problems related to these objects.