search of hadamard matrices by turyn sequences

Abstract

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 dierence 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 nd Hadamard matrices from Turyn sequences. We found excellent solutions with this search method.