Talk:Tables

Some APN functions $CCZ-$equivalent to gold functions and EA-enequivalent to power functions over $\mathbb {F} _{2^{n}}$

Some APN functions $CCZ-$equivalent to gold functions and EA-enequivalent to power functions over $\mathbb {F} _{2^{n}}$ (constructed in

Functions	Conditions	$d^{\circ }$
$x^{2^{i}+1}+(x^{2^{i}}+tr_{n}(1)+1)tr(x^{2^{i}+1}+xtr_{n}(1))$	$n\geq 4,\ gcd(i,n)=1$	3
$x+tr_{n/3}(x^{2(2^{i}+1)}+x^{4(2^{i}+1)})+tr_{n}(x)\,tr_{n/3}(x^{2^{i}+1}+x^{2^{2i}(2^{i}+1)})^{2^{i}+1}$	$6|n,\ gcd(i,n)=1$	4
$x^{2^{i}+1}+tr_{n/m}(x^{2^{i}+1})+x^{2^{i}}tr_{n/m}(x)+xtr_{n/m}(x)^{2^{i}}+[tr_{n/m}(x)^{2^{i}+1}+tr_{n/m}(x^{2^{i}+1})+tr_{n/m}(x)]^{\frac {1}{2^{i}+1}}(x^{2^{i}}+tr_{n/m}(x)^{2^{i}}+1)+[tr_{n/m}(x)^{2^{i}+1}+tr_{n/m}(x^{2^{i}+1})+tr_{n/m}(x)]^{\frac {2^{i}}{2^{i}+1}}(x+tr_{n/m}(x))$	$m\neq n,\ n\ odd,\ m|n,\ gcd(i,n)=1$	$m+2$