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.
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 
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/
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     author = {Nan, Jizhu and Qin, Yufang},
     title = {Structure of unitary groups over finite group rings and its application},
     journal = {Czechoslovak Mathematical Journal},
     pages = {495--512},
     year = {2010},
     volume = {60},
     number = {2},
     mrnumber = {2657964},
     zbl = {1208.20047},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a14/}
}
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