Two new infinite classes of APN functions
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In this paper, we present two new infinite classes of APN functions over _2^2m and _2^3m, respectively. The first one is with bivariate form and obtained by adding special terms, ∑(a_ix^2^iy^2^i,b_ix^2^iy^2^i), to a known class of APN functions by Göloǧlu over _2^m^2. The second one is of the form L(z)^2^m+1+vz^2^m+1 over _2^3m, which is a generalization of one family of APN functions by Bracken et al. [Cryptogr. Commun. 3 (1): 43-53, 2011]. The calculation of the CCZ-invariants Γ-ranks of our APN classes over _2^8 or _2^9 indicates that they are CCZ-inequivalent to all known infinite families of APN functions. Moreover, by using the code isomorphism, we see that our first APN family covers an APN function over _2^8 obtained through the switching method by Edel and Pott in [Adv. Math. Commun. 3 (1): 59-81, 2009].
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