On D4t-Cocyclic Hadamard Matrices
Journal of Combinatorial Designs2016Vol. 24(8), pp. 352–368
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Abstract
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 . Using this characterization, new classification results for certain cohomology classes of cocycles over are obtained, extending existing exhaustive calculations for cocyclic Hadamard matrices over from order 36 to order 44. We also define some transformations over coboundaries, which preserve orthogonality of -cocycles. These transformations are shown to correspond to Horadam's bundle equivalence operations enriched with duals of cocycles.
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