本文利用有限域上的辛几何来构造一种新的 Cartesian认证码 ,在文中计算了认证码的参数 ,并在假定按照等概率分布来选择编码规则下 ,计算了成功模仿攻击概率 PI 和成功替换攻击概率 Ps,它们都达到了最优或接近最优 ,为实现一些好的实用认证技术在理论上提供了可靠的基础 ,同时也给出了构造 Cartesian认证码的技巧 ,进而为利用建立在其它典型群上的几何构造 Cartesian认证码提供了可以借鉴的新方法 In this paper, a new Cartesian authentication code is constructed by using the symplectic geometry over a finite field. The parameters of the authentication code are calculated in this paper. Under the assumption that the coding rules are chosen according to the equal probability distribution, the probability of successfully imitating the attack probability PI and the successful replacement Attack probability Ps, all of them are optimal or nearly optimal, in order to achieve some good practical authentication technology in theory to provide a reliable basis, but also given the skills to construct Cartesian authentication code, and then use to establish other Geometric Constructions on Typical Populations Cartesian authentication codes offer new ways to learn