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

Cocyclic construction has been successfully used for Hadamard matrices of order n. These (-1,1)-matrices satisfy that HHT=HTH=nI 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 n≡2mod4). More concretely, we give a reformulation of the criterion to decide whether or not the 2t×2t determinant with entries ±1 attains the Ehlich-Wojtas’ bound in the D2t-cocyclic framework. We also provide some algorithms for constructing D2t-cocyclic matrices with large determinants and some explicit calculations up to t=19.