William P. Orrick
Published 2005-07-25, updated 2007-09-30Version 4
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 18,292,717.
Comments: 23 pages. v4: revised in response to referee comments; added section on coding theory classification; updated numerical results
The codes and the lattices of Hadamard matrices
Spin models constructed from Hadamard matrices
Some new near-normal sequences
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