Switching operations for Hadamard matrices

Details Switching operations for Hadamard matrices Switching operations for Hadamard matrices

2005-07-25

arxiv.org/abs/math/0507515v4

Mathematics

Combinatorics

23 pages. v4: revised in response to referee comments; added section on coding theory classification; updated numerical result

Scientific paper

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.

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