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… 

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