Known infinite families of quadratic APN polynomials over GF(2^n)

$N^{\circ }$	Functions	Conditions	References
C1-C2	$x^{2^{s}+1}+u^{2^{k}-1}x^{2^{ik}+2^{mk+s}}$	$n=pk,\gcd(k,3)=\gcd(s,3k)=1,p\in \{3,4\}$, $i=sk{\bmod {p}},m=p-i,n\geq 12,u{\text{ primitive in }}\mathbb {F} _{2^{n}}^{*}$
C3	$sx^{q+1}+x^{2^{i}+1}+x^{q(2^{i}+1)}+cx^{2^{i}q+1}+c^{q}x^{2^{i}+q}$	$q=2^{m},n=2m,gcd(i,m)=1,c\in \mathbb {F} _{2^{n}},s\in \mathbb {F} _{2^{n}}\setminus \mathbb {F} _{q}$, $X^{2^{i}+1}+cX^{2^{i}}+c^{q}X+1{\text{ has no solution }}x{\text{ s.t. }}x^{q+1}=1$
C4	$x^{3}+a^{-1}\mathrm {Tr} _{n}(a^{3}x^{9})$	$a\neq 0$
C5	$x^{3}+a^{-1}\mathrm {Tr} _{n}^{3}(a^{3}x^{9}+a^{6}x^{18})$	$3|n$, $a\neq 0$
C6	$x^{3}+a^{-1}\mathrm {Tr} _{n}^{3}(a^{6}x^{18}+a^{12}x^{36})$	$3|n,a\neq 0$
C7-C9	$ux^{2^{s}+1}+u^{2^{k}}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^{k}+1}x^{2^{s}+2^{k+s}}$	$n=3k,\gcd(k,3)=\gcd(s,3k)=1,v,w\in \mathbb {F} _{2^{k}}$, $vw\neq 1,3|(k+s),u{\text{ primitive in }}\mathbb {F} _{2^{n}}^{*}$
C10	$(x+x^{2{^{m}}})^{2^{k}+1}+u'(ux+u^{2^{m}}x^{2^{m}})^{(2^{k}+1)2^{i}}+u(x+x^{2^{m}})(ux+u^{2^{m}}x^{2^{m}})$	$n=2m,m\geqslant 2$ even, $\gcd(k,m)=1$ and $i\geqslant 2$ even, $u{\text{ primitive in }}\mathbb {F} _{2^{n}}^{*},u'\in \mathbb {F} _{2^{m}}{\text{ not a cube }}$
C11	$L(x)^{2^{i}}x+L(x)x^{2^{i}}$	$n=km,m>1,\gcd(n,i)=1,L(x)=\sum _{j=0}^{k-1}a_{j}x^{2^{jm}}$ satisfies the conditions in Theorem 3.6 of [7]
C12	$ut(x)(x^{q}+x)+t(x)^{2^{2i}+2^{3i}}+at(x)^{2^{2i}}(x^{q}+x)^{2^{i}}+b(x^{q}+x)^{2^{i}+1}$	$n=2m,q=2^{m},\gcd(m,i)=1,t(x)=u^{q}x+x^{q}u$, $X^{2^{i}+1}+aX+b{\mbox{ has no solution over }}\mathbb {F} _{2^{m}}$
C13	$x^{3}+a(x^{2^{i}+1})^{2^{k}}+bx^{3\cdot 2^{m}}+c(x^{2^{i+m}+2^{m}})^{2^{k}}$	$n=2m=10,(a,b,c)=(\beta ,1,0,0),i=3,k=2,\beta {\text{ primitive in }}\mathbb {F} _{2^{2}}$
		$n=2m,m\ odd,3\nmid m,(a,b,c)=(\beta ,\beta ^{2},1),\beta {\text{ primitive in }}\mathbb {F} _{2^{2}}$, $i\in \{m-2,m,2m-1,(m-2)^{-1}\mod n\}$