On Hadamard-Type Matrices of Even Orders over Finite Fields

Hadamard-type matrix on GF(p) is a square matrix H that have its elements on GF(p) and satisfies HHT = nI under modulo p, where n represents the order of the matrix and I is an identity matrix. Any additions and multiplications should be executed under modulo p. It has been shown that the order of an arbitrary Hadamard-type matrix of odd order is limited to a quadratic residue of a given prime p. In this study, we show that it is possible to generate a Hadamard-type matrix of any even order.