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, that 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.
@article{arxiv.2002.00673,
title = {A lower bound on the number of inequivalent APN functions},
author = {Christian Kaspers and Yue Zhou},
journal= {arXiv preprint arXiv:2002.00673},
year = {2020}
}