Publication Details

This book chapter was originally published as Georgiou, S, Koukouvinos, C and Seberry, J, Hadamard matrices, orthogonal designs and construction algorithm, in Wallis, WD (ed), Designs 2002: Further Combinatorial and Constructive Design Theory, Kluwer Academic Publishers, Norwell, Massachusetts, 2002, 133-205. Original book available here.


We discuss algorithms for the construction of Hadamard matrices. We include discussion of construction using Williamson matrices, Legendre pairs and the discret Fourier transform and the two circulants construction. Next we move to algorithms to determine the equivalence of Hadamard matrices using the profile and projections of Hadamard matrices. A summary is then given which considers inequivalence of Hadamard matrices of orders up to 44. The final two sections give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array.