Switching Operations for Hadamard Matrices

William P. Orrick
2008 SIAM Journal on Discrete Mathematics  
We define several operations that switch substructures of Hadamard matrices thereby producing new, generally inequivalent, Hadamard matrices. These operations have application to the enumeration and classification of Hadamard matrices. To illustrate their power, we use them to greatly improve the lower bounds on the number of equivalence classes of Hadamard matrices in orders 32 and 36 to 3,578,006 and 4,745,357.
doi:10.1137/050641727 fatcat:r5bnjetgm5aqni2f6eyvqngasy