# New Infinite Families of Perfect Quaternion Sequences and Williamson Sequences

@article{Bright2020NewIF, title={New Infinite Families of Perfect Quaternion Sequences and Williamson Sequences}, author={Curtis Bright and Ilias S. Kotsireas and Vijay Ganesh}, journal={IEEE Transactions on Information Theory}, year={2020}, volume={66}, pages={7739-7751} }

We present new constructions for perfect and odd perfect sequences over the quaternion group <inline-formula> <tex-math notation="LaTeX">$Q_{8}$ </tex-math></inline-formula>. In particular, we show for the first time that perfect and odd perfect quaternion sequences exist in all lengths <inline-formula> <tex-math notation="LaTeX">$2^{t}$ </tex-math></inline-formula> for <inline-formula> <tex-math notation="LaTeX">$t\geq 0$ </tex-math></inline-formula>. In doing so we disprove the quaternionic…

## Topics from this paper

## 3 Citations

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Research Statement of Curtis Bright

- 2019

My research focuses on automating mathematics by developing new efficient techniques for solving mathematical conjectures that require extremely large searches. To this end, my research combines the…

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