On D4t-Cocyclic Hadamard Matrices

In this paper, we describe some necessary and sufficient conditions for a set of coboundaries to yield a cocyclic Hadamard matrix over the dihedral group D4t. Using this characterization, new classification results for certain cohomology classes of cocycles over D4t are obtained, extending existing exhaustive calculations for cocyclic Hadamard matrices over D4t from order 36 to order 44. We also define some transformations over coboundaries, which preserve orthogonality of D4t -cocycles. These transformations are shown to correspond to Horadam’s bundle equivalence operations enriched with duals of cocycles.Junta de Andalucía FQM-01