Structure of unitary groups over finite group rings and its application

In this paper, we determine all the normal forms of Hermitian matrices over finite group rings R = F_q²GR = {F_{{q^2}}}G, where q = p ^α , G is a commutative p-group with order p ^β . Furthermore, using the normal forms of Hermitian matrices, we study the structure of unitary group over R through investigating its BN-pair and order. As an application, we construct a Cartesian authentication code and compute its size parameters.