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On D 4 t ‐Cocyclic Hadamard Matrices
Author(s) -
Álvarez Víctor,
Armario José Andrés,
Frau María Dolores,
Gudiel Félix,
Güemes Maria Belén,
Osuna Amparo
Publication year - 2016
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21510
Subject(s) - mathematics , hadamard transform , dual polyhedron , complex hadamard matrix , hadamard matrix , dihedral group , pure mathematics , combinatorics , equivalence (formal languages) , order (exchange) , hadamard three lines theorem , algebra over a field , group (periodic table) , mathematical analysis , finance , economics , chemistry , organic chemistry
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 D 4 t . Using this characterization, new classification results for certain cohomology classes of cocycles over D 4 t are obtained, extending existing exhaustive calculations for cocyclic Hadamard matrices over D 4 tfrom order 36 to order 44. We also define some transformations over coboundaries, which preserve orthogonality of D 4 t ‐cocycles. These transformations are shown to correspond to Horadam's bundle equivalence operations enriched with duals of cocycles.