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Equivalences of Zt×Z22-cocyclic Hadamard matrices


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Opened Access Equivalences of Zt×Z22-cocyclic Hadamard matrices
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Author: Álvarez Solano, Víctor
Gudiel Rodríguez, Félix
Güemes Alzaga, María Belén
Horadam, K.J.
Rao, A.
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2015
Document type: Article
Abstract: One of the most promising structural approaches to resolving the Hadamard Conjecture uses the family of cocyclic matrices over Zt × Z2 2. Two types of equivalence relations for classifying cocyclic matrices over Zt × Z2 2 have been found. Any cocyclic matrix equivalent by either of these relations to a Hadamard matrix will also be Hadamard. One type, based on algebraic relations between cocycles over any fi- nite group, has been known for some time. Recently, and independently, a second type, based on four geometric relations between diagrammatic visualisations of cocyclic matrices over Zt × Z2 2, has been found. Here we translate the algebraic equivalences to diagrammatic equivalences and show one of the diagrammatic equivalences cannot be obtained this way. This additional equivalence is shown to be the geometric translation of matrix transposition.
Cite: Álvarez Solano, V., Gudiel Rodríguez, F., Güemes Alzaga, M.B., Horadam, K.J. y Rao, A. (2015). Equivalences of Zt×Z22-cocyclic Hadamard matrices. Cornell University.
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