On ‐Cocyclic Hadamard Matrices |
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| Authors: | Víctor Álvarez José Andrés Armario María Dolores Frau Félix Gudiel Maria Belén Güemes Amparo Osuna |
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| Institution: | 1. Department of Applied Mathematics 1, University of Seville, Seville, Spain;2. Department of Algebra, University of Seville, Seville, Spain |
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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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| Keywords: | Hadamard matrix cocyclic matrix Ito's type Q Hadamard matrix shift equivalence bundle |
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