On Mutually Orthogonal Extraordinary Supersquares

Let Fd be a finite field with d elements. Extraordinary subgroups in Fd x Fd play an important role in the field of quantum information theory. It can be ap-plied to the study of mutually unbiased bases. In 2013, Ghiu et al. introduced the concept of supersquare of order d which is related to extraordinary sub-groups. They have given a method of construction of the mutually orthogonal supersquares, and determined all the complete sets of mutually orthogonal ex-traordinary supersquares (MOES) of order 4 and 8. In this thesis, we present the construction of a complete set of MOES of order pn where p is a prime. We also determine all the complete sets of MOES of order 9.