Some APN functions CCZ-equivalent to x^3 + tr n(x^9) and CCZ-inequivalent to the Gold functions over GF(2^n)

Some APN functions CCZ-equivalent to $x^{3}+{\mathrm {T} r}_{n}(x^{9})$ and CCZ-inequivalent to the Gold functions over $\mathbb {F} _{2^{n}}$.

$N^{\circ }$	Functions	Conditions	$d^{\circ }$
$1$	$x^{3}+{\mathrm {T} r}_{n}(x^{9})+(x^{2}+x){\mathrm {T} r}_{n}(x^{3}+x^{9})$	$n\geqslant 5$ odd, $\gcd(i,n)=1$	$3$
$2$	$x^{3}+{\mathrm {T} r}_{n}(x^{9})+(x^{2}+x+1){\mathrm {T} r}_{n}(x^{3})$	$n\geqslant 4$ even, $\gcd(i,n)=1$	$3$
$3$	${\Big (}x+{\mathrm {T} r}_{n}^{3}(x^{6}+x^{12})+{\mathrm {T} r}_{n}(x){\mathrm {T} r}_{n}^{3}(x^{3}+x^{12}){\Big )}^{3}+$ ${\mathrm {T} r}_{n}{\Big (}\left(x+{\mathrm {T} r}_{n}^{3}(x^{6}+x^{12})+{\mathrm {T} r}_{n}(x){\mathrm {T} r}_{n}^{3}(x^{3}+x^{12})\right)^{9}{\Big )}$	$6|n$, $\gcd(i,n)=1$	$4$
$4$	$\left(x^{\frac {1}{3}}+{\mathrm {T} r}_{n}^{3}(x+x^{4})\right)^{-1}+{\mathrm {T} r}_{n}\left(\left(\left(x^{\frac {1}{3}}+{\mathrm {T} r}_{n}^{3}(x+x^{4})\right)^{-1}\right)^{9}\right)$	$3|n$, $n$ odd	$4$