New families of quaternionic Hadamard matrices

Barrera Acevedo, Santiago; Dietrich, Heiko; Lionis, Corey

doi:10.26181/26065735.v1

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New families of quaternionic Hadamard matrices

journal contribution

posted on 2024-07-03, 23:36 authored by Santiago Barrera AcevedoSantiago Barrera Acevedo, Heiko Dietrich, Corey Lionis

Abstract: A quaternionic Hadamard matrix (QHM) of order n is an matrix H with non-zero entries in the quaternions such that , where and denote the identity matrix and the conjugate-transpose of H, respectively. A QHM is dephased if all the entries in its first row and first column are 1, and it is non-commutative if its entries generate a non-commutative group. The aim of our work is to provide new constructions of infinitely many (non-commutative dephased) QHMs; such matrices are used by Farkas et al. (IEEE Trans Inform Theory 69(6):3814–3824, 2023) to produce mutually unbiased measurements.

History

Publication Date

2024-06-18

Journal

Designs, Codes and Cryptography

Pagination

15p.

Publisher

Springer Science and Business Media LLC

ISSN

0925-1022

Rights Statement

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