这份报纸给多项式在特征 2 的有限的地上从颠倒的 Dickson 多项式和 monomials 的作文导出的 Dembowski-Ostrom 的一个完整的分类。作者也在所有之中分类几乎完美的非线性的功能当时,如此的 Dembowski-Ostrom 多项式基于一个将军结果描述一个任意的线性化的多项式的作文并且一表格 \ 单项({ x ^{ 1 +{ 2 ^\alpha }}}\) 是几乎完美的非线性。结果,几乎完美的非线性的功能源于颠倒的 Dickson 多项式都被扩大到著名金牌的仿射的等价物工作。
This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almost perfect nonlinear functions among all such Dembowski-Ostrom polynomials based on a general result describing when the composition of an arbitrary linearized polynomial and a monomial of the form x~(2+2~α) is almost perfect nonlinear.It turns out that almost perfect nonlinear functions derived from reversed Dickson polynomials are all extended affine equivalent to the well-known Gold functions.