On the computation of maximum minors of Hadamard matrices

Authors:
C. Koukouvinos;E. Lappas;M. Mitrouli
Affiliations:
Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece;Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece;Department of Mathematics, University of Athens Panepistemiopolis 15784, Athens, Greece
Venue:
Mathematics and Computers in Simulation - Special issue: Applications of computer algebra in science, engineering, simulation and special software
Year:
2004

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Abstract

In this paper, we use an algebraic method to compute the j × j, j = 1, 2,...,n minors of Hadamard matrices of order n. Specifically, we investigate the appearance of maximum values of minors. The presented algorithm is tested for several values of j and for Hadamard matrices of order 20. This algorithm is useful in the study of the growth factor for Hadamard matrices, which is a very interesting unsolved problem in the area of Numerical Analysis.