\input zb-basic \input zb-ioport \iteman{io-port 05987596} \itemau{Kotsireas, I.S.; Koukouvino, C.; Simos, D.E.} \itemti{A meta-software system for orthogonal designs and Hadamard matrices.} \itemso{J. Appl. Math. Inform. 29, No. 5-6, 1571-1581 (2011).} \itemab Summary: 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. The systems of equations arising when we search for inequivalent Hadamard matrices from full orthogonal designs using circulant and symmetric block matrices, can be concisely described using the periodic autocorrelation function of the generators of the block matrices. We use Maple, Magma, C and Unix tools to find many new inequivalent Hadamard matrices. \itemrv{~} \itemcc{} \itemut{circulant block matrices; symmetric block matrices} \itemli{http://www.kcam.biz/contents/table\_contents\_view.php?idx=1280&Len=} \end