Some Anzahl Theorems of Alternate Matrices over Z/pkZ and its Application
环Z/p\+kZ上m阶交错矩阵的计数定理及其应用

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.