%0 Journal Article
%T Some Anzahl Theorems of Alternate Matrices over Z/pkZ and its Application<br>环Z/p\+kZ上m阶交错矩阵的计数定理及其应用
%A Wu Yan
%A <br>琼州大学数学系
%A 东北师范大学数学系
%J 数学物理学报(A辑)
%D 2004
%I 
%X Let \$W\-m(R)\$  be the set of alternate matrices over \$Z/p\+kZ\$ with order  \$m\$, where \$m≥2,p\$ is aprime and \$k>1\$. By determining the normal form of alternate matrices over\$Z/p\+kZ,\$ the compute \$n(2r,2t,\{r\-1,\:,r\-1\}TXX}]DD(X]s\-1DD)],\:,\{r\-l,\:,r\-l\}TXX}]DD(X]s\-lDD)])\$  and the number of the orbits of \$W\-m(R)\$, where \$W(2r,2t,\{r\-1,\:,r\-1\}TXX}]DD(X]s\-1DD)],\:,\{r\-l,\:,r\-l\}TXX}]DD(X]s\-lDD)])\$   denotes the set of all the alternate matrices with order \$m\$ and the invariant factors of them are \$(2r,2t,\{r\-1,\:,r\-1\}TXX}]DD(X]s\-1DD)],\:,\{r\-l,\:,r\-l\}TXX}]DD(X]s\-lDD)]),\$  and  \$(2r,2t,\{r\-1,\:,r\-1\}TXX}]DD(X]s\-1DD)],\:,\{r\-l,\:,r\-l\}TXX}]DD(X]s\-lDD)])\$ denotes the number of elements in  \$W(2r,2t,\{r\-1,\:,r\-1\}TXX}]DD(X]s\-1DD)],\:, \{r\-l,\:,r\-l\}TXX}]DD(X]s\-lDD)]), ∑DD(]l]i=1DD)]s\-i=t. \$ Furthermore, using the normal form of alternate matrices, the authors construct a Cartesian authentication code and compute the parameters of Cartesian authentication code.
%K Normal form of alternate matrix
%K Anzahl theorems
%K Orbit
%K Finite local ring
%K Authentication code<br>交错矩阵标准形
%K 计数定理
%K 轨道
%K 有限局部环
%K 认证码
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=67B41929FEE54EC6&yid=D0E58B75BFD8E51C&vid=B91E8C6D6FE990DB&iid=38B194292C032A66&sid=160561E9A96393DE&eid=A5B34D9E8FDA439A&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=5