本文在有限域上的二维向量空间中构造了一个带约束的强部分平衡设计，在此基础上构造了完善分裂认证码.首先，借助方程组的理论构造了一个强部分平衡t-设计，得到了第一类分裂认证码.然后对第一类构造增加限制条件，得到了第二类分裂认证码.分别计算了两类认证码的r-阶欺骗攻击成功概率，并证明了它们分别是I型和Ⅱ型的完善认证码.最后，分析了所构造认证码的性能.通过对具体实例的编码矩阵进行数值仿真，验证了本文构造的合理性和相应结论的正确性.通过与相关文献的结果进行对比，得出如下结论：本文信源数目较多，各阶欺骗攻击成功概率都达到最小；且所用理论较基础，编码算法更简单，模拟仿真易于实现.因此本文所构造的认证码，无论从传送信息量还是从安全性与实用性的角度来看，均具有一定的优势.
In this paper, we propose a restricted strongly partially-balanced t-design in a finite two-dimension vector space, and construct a perfect splitting authentication code on the basis of this design. First, based on the theory of equations, a strongly partially-balanced t-design is constructed, and directly one type of splitting authentication codes is obtained. Second, one more type of authentication codes is generated by adding constraints to the above construction process. The two types of codes are proved perfect on splitting authentication by calculating their r-order probabilities of successful spoofing attacks respectively. Finally, the performances of two types of codes are analyzed. By simulations with a specific example, the rationality and validity of the construction approaches are verified. Compared with previous works, it is concluded that in this method, the successful probability of each order deception attack could reach the minimum by using large number of sources, and that the coding algorithm and simulation are easy to implement due to its simple theoretical basis. Therefore, the code constructed in this paper is competitive in terms of amount of transmitting information, security and practicability.
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