English

On Some Quaternionic Hadamard Matrices of Small Order

Combinatorics 2022-03-08 v2 Rings and Algebras

Abstract

We introduce Hadamard matrices whose entries are quaternionic. We then go on to provide classification of quaternionic Hadamard matrices of circulant core of orders 2 through 5. We also introduce quaternionic Hadamard matrices of Butson type and ways to create quaternionic Hadamard matrices from real and complex Hadamard matrices. Examples are shown that showcase how Hadamard matrices over the quaternions are richer than Hadamard matrices over the complex numbers.

Keywords

Cite

@article{arxiv.2112.09613,
  title  = {On Some Quaternionic Hadamard Matrices of Small Order},
  author = {Logan M. Higginbotham and Chase T. Worley},
  journal= {arXiv preprint arXiv:2112.09613},
  year   = {2022}
}

Comments

30 pages, submitted for publication

R2 v1 2026-06-24T08:22:14.721Z