In this paper, we study the relationship between algebraic manipulation detection (AMD) codes and highly nonlinear functions. As applications, on one hand, a generic construction for systematic AMD codes is introduced based on highly nonlinear functions. Systematic AMD codes with new parameters can be generated from known highly nonlinear functions. Especially, several infinite classes of optimal systematic AMD codes, some with asymptotically optimal tag size, can be constructed. On the other hand, systematic AMD codes are used to construct highly nonlinear functions. The known construction by Cramer et al. (2008) for systematic AMD codes turns out to be based on a special kind of functions with high nonlinearity.

在本文中，我们研究了代数操作检测（AMD）代码与高度非线性函数之间的关系。一方面，作为应用，基于高度非线性函数引入了系统AMD代码的通用构造。具有新参数的系统AMD代码可以从已知的高度非线性函数生成。特别是，可以构造出几类无限的最优系统AMD代码，其中一些具有渐近最优标签大小。另一方面，系统的AMD代码用于构造高度非线性的函数。Cramer等人的已知结构。（2008年）的系统AMD代码被证明是基于一种具有高度非线性的特殊功能。