Construction of the mutually orthogonal extraordinary supersquares

• Autorzy: Cristian Ghiu , Iulia Ghiu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Latin squares; Finite fields

Kategorie tematyczne

• 05B15: Orthogonal arrays, Latin squares, Room squares
• 12E20: Finite fields (field-theoretic aspects)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 2
• Strony: 337-348

Daty

wydano

2014-02-01

online

2013-11-21

Twórcy

autor

Cristian Ghiu

• University Politehnica of Bucharest

autor

Iulia Ghiu

• University of Bucharest

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0337-2