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On Mutually Orthogonal Extraordinary Supersquares

On Mutually Orthogonal Extraordinary Supersquares Let Fd be the finite field with d elements. Extraordinary subgroups in Fd × Fd play an important role in the field of quantum information theory, especially for the study of mutually unbiased bases. Recently, Ghiu et al. introduced the concept of supersquare of order d which is related to extraordinary subgroups. They have given a method of construction of the mutually orthogonal supersquares, and determined all the complete sets of mutually orthogonal extraordinary supersquares of order 4. In this article, we present the construction of a complete set of mutually orthogonal extraordinary supersquares of order pn where p is a prime. We also determine all the complete sets of mutually orthogonal extraordinary supersquares of order 9. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

On Mutually Orthogonal Extraordinary Supersquares

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Publisher
Springer Journals
Copyright
Copyright © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2021
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-021-1040-x
Publisher site
See Article on Publisher Site

Abstract

Let Fd be the finite field with d elements. Extraordinary subgroups in Fd × Fd play an important role in the field of quantum information theory, especially for the study of mutually unbiased bases. Recently, Ghiu et al. introduced the concept of supersquare of order d which is related to extraordinary subgroups. They have given a method of construction of the mutually orthogonal supersquares, and determined all the complete sets of mutually orthogonal extraordinary supersquares of order 4. In this article, we present the construction of a complete set of mutually orthogonal extraordinary supersquares of order pn where p is a prime. We also determine all the complete sets of mutually orthogonal extraordinary supersquares of order 9.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Oct 1, 2021

Keywords: extraordinary subgroup; supersquare; mutually orthogonal extraordinary supersquare; finite field; 05B15; 12E20

References

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