Calculating cocyclic hadamard matrices in Mathematica: exhaustive and heuristic searches

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