A lower bound on the number of inequivalent APN functions

In this paper, we establish a lower bound on the total number of inequivalent APN functions on the finite field with $2^{2m}$ 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.

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