Computer generation of Hadamard matrices

We develop a computer code that uses elegant bit-manipulation techniques for matrix multiplication and thus facilitates exhaustive generation of Skew-Hadamard matrices. Hadamard matrices are useful in spectroscopic applications (Hadamard transform spectroscopy) and in balanced chemical designs. Application of our code yields several Skew-Hadamard matrices up to order 100 X 100, although the combinatorial complexity of exhaustive generation increases exponentially. Our bit-manipulation-based codes took 124 h of CPU time to perform 7.79334 x 10" matrix multiplications on an IBM RS 6000/560 system to generate all 100 x 100 matrices. This amounts to 5.7 x s of CPU time per matrix multiplication.