The Hadamard conjecture (unsolved since 1867) states that there exists an orthogonal matrix with entries of the same absolute value if and only if the order of the matrix is one, two, or is divisible by four. In the paper we reformulate this conjecture using Hurwitz-Radon word systems. (A Hurwitz-Radon word system is a system of words formed from an alphabet, which is a Klein group, so that the letter wise product of any two different words from the system contains an odd number of the letter b.) We present also algorithms for calculating maximal orthogonal word systems.
Eotvos University Operations Research Technical Report ORR 2009-02, http://www.cs.elte.hu/opres/orr