Abstract

PIZA, Eduardo. Search of Hadamard matrices by Turyn sequences. Rev. Mat [online]. 2011, vol.18, n.2, pp.193-214. ISSN 1409-2433.

In this paper we study the Hadamard matrices and some algorithms to generate them. We review some theoretical aspects about Hadamard's conjecture, which asserts that every positive integer multiple of 4 is a Hadamard number. Then we describe the methods of Kronecker, Sylvester, Paley, Williamson, Goethals-Seidel, Cooper-Wallis, Baumert-Hall, Ehlich and supplementary difference sets. Subsequently we settle the Hadamard sieve: 668 is lowest order for which is unknown if there exist an Hadamard matrix. Finally we propose a simulated annealing algorithms as alternative to find Hadamard matrices from Turyn sequences. We found excellent solutions with this search method.

Keywords : Hadamard matrices; simulated annealing; combinatorial optimization.

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