Abstract
AbstractOur 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.
Reference17 articles.
1. Aly Ahmed S.A.A., Quantum Error Control Codes, PhD thesis, Texas A&M University, 2008
2. Asplund J., Keranen M.S., Mutually orthogonal equitable Latin rectangles, Discrete Math., 2011, 311(12), 1015–1033
3. Bandyopadhyay S., Boykin P.O., Roychowdhury V., Vatan V., A new proof for the existence of mutually unbiased bases, Algorithmica, 2002, 34(4), 512–528
4. Bose R.C., Shrikhande S.S., On the construction of sets of mutually orthogonal Latin squares and the falsity of a conjecture of Euler, Trans. Amer. Math. Soc., 1960, 95(2), 191–209
5. Ghiu I., A new method of construction of all sets of mutually unbiased bases for two-qubit systems, J. Phys. Conf. Ser., 2012, 338, #012008
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献