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 a...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.展开更多
基金This paper is supported by the National Natural Science Foundation of China(Nos.12071226,11931006,12101414).
文摘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.
