Abstract: This paper designs a new class of authentication codes applying the theory of the normal form of matrices.By introducing the ordered partition of natural numbers，all parameters of this scheme are computed.Moreover，the paper assumes that its keys are chosen according to the uniform probability distribution，the two probabilities of successful attacks of the opponents are also computed.

Key words: authentication codes, ordered partition, low triangular Toeplitz matrices

摘要： 运用矩阵的标准型理论设计了一类新的Cartesian认证码，引入自然数的有序分拆计算了该认证码的全部参数。在密钥均匀分布的条件下，分析了该类认证方案被敌手成功攻击的两种概率。

关键词: 认证码, 有序分拆, 下三角Toeplitz矩阵