This paper is dedicated to a question whether the currently known families of quadratic APN polynomials are pairwise different up to CCZ-equivalence. We reduce the list of these families to those CCZ-inequivalent to each other. In particular, we prove that the families of APN trinomials (constructed by Budaghyan and Carlet in 2008) and multinomials (constructed by Bracken et al. 2008) are contained in the APN hexanomial family introduced by Budaghyan and Carlet in 2008. We also prove that a generalization of these trinomial and multinomial families given by Duan et al. (2014) is contained in the family of hexanomials as well.

中文翻译：

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关于二次APN函数的已知族之间的等价性

本文专门针对一个问题，即当前已知的二次APN多项式族在CCZ等效性之前是否成对不同。我们将这些族的列表减少为彼此不等的CCZ。特别是，我们证明了APN三项式（由Budaghyan和Carlet于2008年构建）和多项式（由Bracken等人2008年构成）的族包含在Budaghyan和Carlet在2008年引入的APN六项族中。 Duan等人给出的这些三项式和多项式族的概括。（2014）也包含在十六进制族中。