33 research outputs found
Construction of the mutually orthogonal extraordinary supersquares
Our purpose is to determine the complete set of mutually orthogonal squares
of order , which are not necessary Latin. In this article, we introduce the
concept of supersquare of order , which is defined with the help of its
generating subgroup in . 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 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 mutually orthogonal
Latin squares is only a special case, namely Type I