Structure of unitary groups over finite group rings and its application

summary:In this paper, we determine all the normal forms of Hermitian matrices over finite group rings $R=F_{q^2}G$, where $q=p^{\alpha }$, $G$ is a commutative $p$-group with order $p^{\beta }$. 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