Geodesic
A classification of differentially nonequivalent quadratic APN function in~5 and~6 variables
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 35-36.

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A vector Boolean function $F$ from $\mathbb F_2^n$ to $\mathbb F_2^n$ is called almost perfect nonlinear (APN) if equation $F(x)\oplus F(x\oplus a)=b$ has at most 2 solutions for all vectors $a,b\in\mathbb F_2^n$, where $a$ is non-zero. Two functions $F$ and $G$ are called differentially equivalent if $B_a(F)=B_a(G)$ for all $a\in\mathbb F_2^n$, where $B_a(F)=\{F(x)\oplus F(x\oplus a)\colon x\in\mathbb F_2^n\}$. A classification of differentially non-equivalent quadratic APN function in 5 and 6 variables is obtained. We prove that, for a quadratic APN function $F$ in $n$ variables, $n\leqslant6$, all differentially equivalent to $F$ quadratic functions are represented as $F\oplus A$, where $A$ is an affine function.
Keywords: APN functions, differential equivalence, linear spectrum. 
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     author = {A. A. Gorodilova},
     title = {A classification of differentially nonequivalent quadratic {APN} function in~5 and~6 variables},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {35--36},
     publisher = {mathdoc},
     number = {10},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a12/}
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A. A. Gorodilova. A classification of differentially nonequivalent quadratic APN function in~5 and~6 variables. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 35-36. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a12/

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