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A lower bound on the number of inequivalent APN functions
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2021-10-14 , DOI: 10.1016/j.jcta.2021.105554
Christian Kaspers , Yue Zhou

In this paper, we establish a lower bound on the total number of inequivalent APN functions on the finite field with 22m elements, where m is even. We obtain this result by proving that the APN functions introduced by Pott and the second author [22], which depend on three parameters k, s and α, are pairwise inequivalent for distinct choices of the parameters k and s. Moreover, we determine the automorphism group of these APN functions.



中文翻译:

不等价 APN 函数数量的下限

在本文中,我们建立了有限域上不等价 APN 函数总数的下界,其中 22元素,其中m是偶数。我们通过证明 Pott 和第二作者 [22] 引入的 APN 函数(依赖于三个参数ksα )对于参数ks 的不同选择是成对不等价的,从而获得了这个结果。此外,我们确定了这些 APN 函数的自同构群。

更新日期:2021-10-15
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