利用有限域上矩阵的标准型构作卡氏认证码

本文利用有限域上长方矩阵的等价标准型构作了一个笛卡尔认证码并计算出该码的所有参数．进而，假定编码规则按照统一的概率分布所选取，该码的成功伪造与成功替换的最大概率Ｐ_Ｉ与Ｐ_Ｓ亦被计算出来．

Using Normal Form of Matrices over Finite Fields to Construct Cartesian Authentication Codes

In this paper, one construction of Cartesian authentication codes from the normal form of matrices over finite fields are presented and its size parameters are computed. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the P_I and P_S, which denote the largest probabilities of a successful impersonation attack and of a successful substitution attack respectively, of these codes are also computed.