Improving the lower bounds on inequivalent Hadamard matrices through orthogonal designs and meta-programming techniques

In this paper, we construct inequivalent Hadamard matrices based on several new and old full orthogonal designs, using circulant and symmetric block matrices. Not all orthogonal designs produce inequivalent Hadamard matrices, because the corresponding systems of equations do not possess solutions. In addition, we give some new constructions for orthogonal designs derived from sequences with zero autocorrelation. The orthogonal designs used to construct the inequivalent Hadamard matrices are produced from theoretical and algorithmic constructions.