A lower bound on the number of inequivalent APN functions

02/03/2020

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by   Christian Kaspers, et al.

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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.