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On higher dimensional cocyclic Hadamard matrices


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Opened Access On higher dimensional cocyclic Hadamard matrices

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Author: Álvarez Solano, Víctor
Armario Sampalo, José Andrés
Frau García, María Dolores
Real Jurado, Pedro
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2015
Published in: Applicable Algebra in Engineering, Communication and Computing, 26 (1), 191-206.
Document type: Article
Abstract: Provided that a cohomological model for G is known, we describe a method for constructing a basis for n-cocycles over G, from which the whole set of n-dimensional n-cocyclic matrices over G may be straightforwardly calculated. Focusing in the case n=2 (which is of special interest, e.g. for looking for cocyclic Hadamard matrices), this method provides a basis for 2-cocycles in such a way that representative 2-cocycles are calculated all at once, so that there is no need to distinguish between inflation and transgression 2-cocycles (as it has traditionally been the case until now). When n>2, this method provides an uniform way of looking for higher dimensional n-cocyclic Hadamard matrices for the first time. We illustrate the method with some examples, for n=2,3. In particular, we give some examples of improper 3-dimensional 3-cocyclic Hadamard matrices.
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