Calculating cocyclic hadamard matrices in mathematica: exhaustive and heuristic searches

Authors:
V. Álvarez;J. A. Armario;M. D. Frau;P. Real
Affiliations:
Dpto. Matemática Aplicada I, Universidad de Sevilla, Sevilla, Spain;Dpto. Matemática Aplicada I, Universidad de Sevilla, Sevilla, Spain;Dpto. Matemática Aplicada I, Universidad de Sevilla, Sevilla, Spain;Dpto. Matemática Aplicada I, Universidad de Sevilla, Sevilla, Spain
Venue:
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Year:
2006

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Abstract

We describe a notebook in Mathematica which, taking as input data a homological model for a finite group G of order |G| = 4t, performs an exhaustive search for constructing the whole set of cocyclic Hadamard matrices over G. Since such an exhaustive search is not practical for orders 4t ≥28, the program also provides an alternate method, in which an heuristic search (in terms of a genetic algorithm) is performed. We include some executions and examples.