Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1

The following tables list CCZ-inequivalent representatives found by systematically searching for APN functions among all trinomials, quadrinomials, pentanomials and hexanomials with coefficients in $\mathbb {F} _{2}$ over $\mathbb {F} _{2^{n}}$ with $6\leq n\leq 11$ . The tables also list which equivalence class from the functions belong to. Only polynomials inequivalent to power functions are considered. If the polynomial is equivalent to a family from the table of infinite families, this is also listed.

Trinomials

$n$	$N^{\circ }$	Functions	Familiy	Relation to
$6$	$-$	$-$	$-$	$-$
$7$	$7.1$	$x^{20}+x^{6}+x^{3}$	$-$	$Table7:N^{\circ }8.1$
	$7.2$	$x^{34}+x^{18}+x^{5}$	$-$	$7:N^{\circ }2.1$
$8$	$8.1$	$x^{72}+x^{6}+x^{3}$	$N^{\circ }5$	$Table9:N^{\circ }1.3$
	$8.2$	$x^{72}+x^{36}+x^{3}$	$-$	$9:N^{\circ }1.4$
$9$	$-$	$-$	$-$	$-$
$10$	$-$	$-$	$-$	$-$
$11$	$-$	$-$	$-$	$-$

Quadrinomials

$n$	$N^{\circ }$	Functions	Families	Relation to
$6$	$-$	$-$	$-$	$-$
$7$	$7.1$	$x^{72}+x^{40}+x^{12}+x^{3}$	$-$	$Table7:N^{\circ }12.1$
	$7.2$	$x^{33}+x^{17}+x^{12}+x^{3}$	$-$	$7:N^{\circ }2.2$
	$7.3$	$x^{34}+x^{33}+x^{10}+x^{3}$	$-$	$7:N^{\circ }10.1$
	$7.4$	$x^{66}+x^{34}+x^{20}+x^{3}$	$-$	$7:N^{\circ }11.1$
	$7.5$	$x^{68}+x^{18}+x^{5}+x^{3}$	$-$	$7:N^{\circ }8.1$
	$7.6$	$x^{66}+x^{18}+x^{9}+x^{3}$	$-$	$7:N^{\circ }9.1$
$8$	$-$	$-$	$-$	$-$
$9$	$-$	$-$	$-$	$-$
$10$	$-$	$-$	$-$	$-$
$11$	$-$	$-$	$-$	$-$

Pentanomials

$n$	$N^{\circ }$	Functions	Families	Relation to
$6$	$-$	$-$	$-$	$-$
$7$	$7.1$	$x^{68}+x^{40}+x^{24}+x^{6}+x^{3}$	$-$	$Table7:N^{\circ }13.1$
	$7.2$	$x^{65}+x^{20}+x^{18}+x^{6}+x^{3}$	$N^{\circ }5$	$7:N^{\circ }1.2$
	$7.3$	$x^{40}+x^{34}+x^{18}+x^{10}+x^{3}$	$-$	$7:N^{\circ }12.1$
	$7.4$	$x^{48}+x^{40}+x^{10}+x^{9}+x^{3}$	$-$	$7:N^{\circ }2.1$
	$7.5$	$x^{33}+x^{9}+x^{6}+x^{5}+x^{3}$	$-$	$7:N^{\circ }11.1$
	$7.6$	$x^{40}+x^{36}+x^{34}+x^{24}+x^{3}$	$-$	$7:N^{\circ }10.1$
	$7.7$	$x^{24}+x^{10}+x^{9}+x^{6}+x^{3}$	$-$	$7:N^{\circ }2.1$
	$7.8$	$x^{65}+x^{36}+x^{20}+x^{17}+x^{3}$	$-$	$7:N^{\circ }14.1$
	$7.9$	$x^{40}+x^{33}+x^{17}+x^{5}+x^{3}$	$-$	$7:N^{\circ }8.1$
	$7.10$	$x^{36}+x^{33}+x^{18}+x^{9}+x^{5}$	$-$	$7:N^{\circ }10.1$
$8$	$8.1$	$x^{36}+x^{33}+x^{9}+x^{6}+x^{3}$	$-$	$Table9:N^{\circ }1.4$
	$8.2$	$x^{72}+x^{66}+x^{12}+x^{6}+x^{3}$	$N^{\circ }5$	$9:N^{\circ }1.3$
	$8.3$	$x^{130}+x^{66}+x^{40}+x^{12}+x^{3}$	$-$	$9:N^{\circ }6.1$
	$8.4$	$x^{66}+x^{40}+x^{18}+x^{5}+x^{3}$	$-$	$9:N^{\circ }5.1$
$9$	$-$	$-$	$-$	$-$
$10$	$-$	$-$	$-$	$-$
$11$	$11.1$	$x^{12}+x^{10}+x^{9}+x^{5}+x^{3}$	$-$	$-$
	$11.2$	$x^{258}+x^{257}+x^{18}+x^{17}+x^{3}$	$-$	$-$
	$11.3$	$x^{96}+x^{66}+x^{34}+x^{33}+x^{3}$	$-$	$-$
	$11.4$	$x^{80}+x^{68}+x^{65}+x^{17}+x^{5}$	$-$	$-$
	$11.5$	$x^{260}+x^{257}+x^{36}+x^{33}+x^{5}$	$-$	$-$

Hexanomials

$n$	$N^{\circ }$	Functions	Families	Relation to
$6$	$-$	$-$	$-$	$-$
$7$	$7.1$	$x^{34}+x^{33}+x^{12}+x^{6}+x^{5}+x^{3}$	$-$	$Table7:N^{\circ }14.2$
	$7.2$	$x^{40}+x^{24}+x^{20}+x^{9}+x^{5}+x^{3}$	$-$	$7:N^{\circ }14.1$
	$7.3$	$x^{33}+x^{24}+x^{20}+x^{18}+x^{12}+x^{3}$	$-$	$7:N^{\circ }12.1$
	$7.4$	$x^{24}+x^{17}+x^{12}+x^{10}+x^{6}+x^{3}$	$-$	$7:N^{\circ }2.1$
	$7.5$	$x^{40}+x^{34}+x^{18}+x^{17}+x^{5}+x^{3}$	$N^{\circ }5$	$7:N^{\circ }1.2$
	$7.6$	$x^{48}+x^{40}+x^{18}+x^{10}+x^{5}+x^{3}$	$-$	$7:N^{\circ }11.1$
	$7.7$	$x^{40}+x^{12}+x^{10}+x^{9}+x^{5}+x^{3}$	$-$	$7:N^{\circ }2.2$
	$7.8$	$x^{34}+x^{24}+x^{10}+x^{9}+x^{6}+x^{3}$	$-$	$7:N^{\circ }9.1$
	$7.9$	$x^{34}+x^{33}+x^{20}+x^{17}+x^{10}+x^{3}$	$-$	$7:N^{\circ }13.1$
	$7.10$	$x^{36}+x^{33}+x^{24}+x^{9}+x^{6}+x^{3}$	$-$	$7:N^{\circ }10.1$
	$7.11$	$x^{40}+x^{36}+x^{20}+x^{10}+x^{5}+x^{3}$	$-$	$7:N^{\circ }10.2$
	$7.12$	$x^{36}+x^{34}+x^{20}+x^{10}+x^{9}+x^{3}$	$-$	$7:N^{\circ }8.1$
$8$	$8.1$	$x^{68}+x^{34}+x^{17}+x^{12}+x^{9}+x^{3}$	$-$	$Table9:N^{\circ }5.1$
	$8.2$	$x^{72}+x^{40}+x^{34}+x^{20}+x^{12}+x^{3}$	$N^{\circ }5$	$9:N^{\circ }6.1$
	$8.3$	$x^{72}+x^{66}+x^{34}+x^{18}+x^{10}+x^{5}$	$-$	$9:N^{\circ }4.1$
$9$	$-$	$-$	$-$	$-$
$10$	$-$	$-$	$-$	$-$
$11$	$-$	$-$	$-$	$-$