Hadamard matrices of Williamson type: A challenge for Computer Algebra

Authors:
Ilias S. Kotsireas;Christos Koukouvinos
Affiliations:
Wilfrid Laurier University, Department of Physics and Computer Science, 75 University Avenue West, Waterloo, Ontario N2L 3C5, Canada;Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece
Venue:
Journal of Symbolic Computation
Year:
2009

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Abstract

We describe new families of challenging polynomial systems of equations arising in the construction of Hadamard matrices of Williamson type. These systems depend on a parameter and exhibit a number of symmetries. We demonstrate that Genetic Algorithms form a suitable tool to apply to these systems, for which the traditional Computer Algebra methods seem to be inappropriate.