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Construction of the mutually orthogonal extraordinary supersquares

Cristian Ghiu; Iulia Ghiu

Open Mathematics (2014)

  • Volume: 12, Issue: 2, page 337-348
  • ISSN: 2391-5455

Abstract

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Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in 𝔽 d × 𝔽 d . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups in 𝔽 d × 𝔽 d are of great importance in the field of quantum information processing, especially for the study of mutually unbiased bases. We determine the most general complete sets of mutually orthogonal extraordinary supersquares of order 4, which consist in the so-called Type I and Type II. The well-known case of d − 1 mutually orthogonal Latin squares is only a special case, namely Type I.

How to cite

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Cristian Ghiu, and Iulia Ghiu. "Construction of the mutually orthogonal extraordinary supersquares." Open Mathematics 12.2 (2014): 337-348. <http://eudml.org/doc/269028>.

@article{CristianGhiu2014,
abstract = {Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in \[\mathbb \{F\}\_d \times \mathbb \{F\}\_d\] . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups in \[\mathbb \{F\}\_d \times \mathbb \{F\}\_d\] are of great importance in the field of quantum information processing, especially for the study of mutually unbiased bases. We determine the most general complete sets of mutually orthogonal extraordinary supersquares of order 4, which consist in the so-called Type I and Type II. The well-known case of d − 1 mutually orthogonal Latin squares is only a special case, namely Type I.},
author = {Cristian Ghiu, Iulia Ghiu},
journal = {Open Mathematics},
keywords = {Latin squares; Finite fields; extraordinary supersquares; orthogonality; finite fields},
language = {eng},
number = {2},
pages = {337-348},
title = {Construction of the mutually orthogonal extraordinary supersquares},
url = {http://eudml.org/doc/269028},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Cristian Ghiu
AU - Iulia Ghiu
TI - Construction of the mutually orthogonal extraordinary supersquares
JO - Open Mathematics
PY - 2014
VL - 12
IS - 2
SP - 337
EP - 348
AB - Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in \[\mathbb {F}_d \times \mathbb {F}_d\] . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups in \[\mathbb {F}_d \times \mathbb {F}_d\] are of great importance in the field of quantum information processing, especially for the study of mutually unbiased bases. We determine the most general complete sets of mutually orthogonal extraordinary supersquares of order 4, which consist in the so-called Type I and Type II. The well-known case of d − 1 mutually orthogonal Latin squares is only a special case, namely Type I.
LA - eng
KW - Latin squares; Finite fields; extraordinary supersquares; orthogonality; finite fields
UR - http://eudml.org/doc/269028
ER -

References

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