Year: 2019
Type: preprint
Abstract: Let $G$ be a finite group and let $h$ be a positive integer. A $\text{BH}(G,h)$ matrix is a $G$-invariant $|G|\times |G|$ matrix $H$ whose entries are complex $h$th roots of unity such that $HH^*=|G|I_{|G|}$, where $H^*$ denotes the complex conjugate transpose of $H$, and $I_{|G|}$ is the identity matrix of order $|G|$. In this paper, we give three new constructions of $\text{BH}(G,h)$ matrices. The first construction is the first known family of $\text{BH}(G,h)$ matrices in which $G$ does not need to be abelian. The second and the third constructions are two families of $\text{BH}(G,h)$ matrices in which $G$ is a finite local ring.
Source: arXiv (Cornell University)
Author: Duc, Tai Do
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4288409779