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A meta-software system for orthogonal designs and Hadamard matrices. (English) Zbl 1233.05066

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.

MSC:

05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
05B15 Orthogonal arrays, Latin squares, Room squares
68R05 Combinatorics in computer science
68W30 Symbolic computation and algebraic computation

Software:

Maple
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