# Switching Operations for Hadamard Matrices

@article{Orrick2008SwitchingOF, title={Switching Operations for Hadamard Matrices}, author={William P. Orrick}, journal={SIAM J. Discret. Math.}, year={2008}, volume={22}, pages={31-50} }

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.

## 32 Citations

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- MathematicsOpen Syst. Inf. Dyn.
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Basic properties of complex Hadamard matrices are reviewed and a catalogue of inequivalent cases known for the dimensions N = 2, 16, 12, 14 and 16 are presented.

### A Path to Hadamard Matrices

- Computer ScienceAAECC
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### Trades in complex Hadamard matrices Padraig Ó Catháin

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### The quaternary complex Hadamard matrices of orders 10, 12, and 14

- MathematicsDiscret. Math.
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- Mathematics
- 2015

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### Construction, classification and parametrization of complex Hadamard matrices

- Mathematics
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The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent…

### On D4t ‐Cocyclic Hadamard Matrices

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In this paper, we describe some necessary and sufficient conditions for a set of coboundaries to yield a cocyclic Hadamard matrix over the dihedral group D4t . Using this characterization, new…

### Equivalences of Zt×Z22-cocyclic Hadamard matrices

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One of the most promising structural approaches to resolving the Hadamard Conjecture uses the family of cocyclic matrices over Zt × Z 2 2. Two types of equivalence relations for classifying cocyclic…

### Group actions on Hadamard matrices

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- 2008

Faculty of Arts Mathematics Department Master of Literature by Padraig Ó Catháin Hadamard matrices are an important item of study in combinatorial design theory. In this thesis, we explore the theory…

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