The maximal determinant of cocyclic (−1, 1)-matrices over D2t

Abstract

Cocyclic construction has been successfully used for Hadamard matrices of order n. These -matrices satisfy that and give the solution to the maximal determinant problem when or a multiple of 4. In this paper, we approach the maximal determinant problem using cocyclic matrices when . More concretely, we give a reformulation of the criterion to decide whether or not the determinant with entries attains the Ehlich-Wojtas’ bound in the -cocyclic framework. We also provide some algorithms for constructing -cocyclic matrices with large determinants and some explicit calculations up to .