Geodesic
Structure of unitary groups over finite group rings and its application
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 495-512

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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.
Classification : 19G24, 20E42, 94A60
Keywords: finite group ring; BN-pair; authentication code 
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     author = {Nan, Jizhu and Qin, Yufang},
     title = {Structure of unitary groups over finite group rings and its application},
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     pages = {495--512},
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     zbl = {1208.20047},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2010__60_2_a14/}
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Nan, Jizhu; Qin, Yufang. Structure of unitary groups over finite group rings and its application. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 495-512. http://geodesic.mathdoc.fr/item/CMJ_2010__60_2_a14/