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Structure of unitary groups over finite group rings and its application

Jizhu Nan; Yufang Qin — 2010

Czechoslovak Mathematical Journal

In this paper, we determine all the normal forms of Hermitian matrices over finite group rings $R = F_{q^{2}} G$ , 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.

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