In this article, we study algebraic decompositions and secondary constructions of almost perfect nonlinear (APN) functions. In many cases, we establish precise criteria which characterize when certain modifications of a given APN function yield new ones. Furthermore, we show that some of the newly constructed functions are extended-affine inequivalent to the original ones.

翻译：本文研究了几乎完美非线性（APN）函数的代数分解与二次构造方法。我们在多种情形下建立了精确的判别准则，用以刻画对给定APN函数进行特定修改后能否生成新APN函数的条件。此外，我们证明了部分新构造的函数与原始函数在扩展仿射意义下不等价。