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The problem of finding APN permutations of ${\mathbb F}_{2^n}$ where $n$ iseven and $n>6$ has been called the Big APN Problem. Li, Li, Helleseth and Qurecently characterized APN functions defined on ${\mathbb F}_{q^2}$ of the form$f(x)=x^{3q}+a_1x^{2q+1}+a_2x^{q+2}+a_3x^3$, where $q=2^m$ and $m\ge 4$. Wewill call functions of this form Kim-type functions because they generalize theform of the Kim function that was used to construct an APN permutation of${\mathbb F}_{2^6}$. We extend the result of Li, Li, Helleseth and Qu byproving that if a Kim-type function $f$ is APN and $m\ge 4$, then $f$ is affineequivalent to one of two Gold functions $G_1(x)=x^3$ or $G_2(x)=x^{2^{m-1}+1}$.Combined with the recent result of G\"{o}lo\u{g}lu and Langevin who provedthat, for even $n$, Gold APN functions are never CCZ equivalent topermutations, it follows that for $m\ge 4$ Kim-type APN functions on ${\mathbbF}_{2^{2m}}$ are never CCZ equivalent to permutations.

Kim-type APN functions are affine equivalent to Gold functions