In this paper, a class of linear authentication codes with secrecy are constructed, which have simple encoding rules and are easy to implement. Based on the special Weil sum, the maximum success probabilities of substitution attack and impersonation attack are calculated, and these codes are proven to be asymptotically optimal with respect to certain bounds.

翻译：本文构造了一类具有保密性的线性认证码，该类编码具有简洁的编码规则且易于实现。基于特殊的Weil和，计算了替代攻击和伪装攻击的最大成功概率，并证明了这些码关于某些界是渐近最优的。