CCZ-inequivalent representatives from the known APN families for dimensions up to 11

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CCZ-inequivalent APN Functions over [math]\displaystyle{ \mathbb{F}_{2^n} }[/math] from the Known APN Classes for [math]\displaystyle{ 6\leqslant n \leqslant 11 }[/math]

Dimension [math]\displaystyle{ N^\circ }[/math] Functions Equivalent to Walsh spectrum Γ-rank Δ-rank
[math]\displaystyle{ 6 }[/math] [math]\displaystyle{ 6.1 }[/math] [math]\displaystyle{ x^3 }[/math] [math]\displaystyle{ Gold }[/math] Gold 1102 94
[math]\displaystyle{ 6.2 }[/math] [math]\displaystyle{ x^{24}+ax^{17}+a^8x^{10}+ax^9+x^3 }[/math] [math]\displaystyle{ C3 }[/math] Gold 1146 94
[math]\displaystyle{ 6.3 }[/math] [math]\displaystyle{ ax^3+x^{17}+a^4x^{24} }[/math] [math]\displaystyle{ C7-C9 }[/math] Gold 1166 96
[math]\displaystyle{ 7 }[/math] [math]\displaystyle{ 7.1 }[/math] [math]\displaystyle{ x^3 }[/math] [math]\displaystyle{ Gold }[/math] Gold 3610 198
[math]\displaystyle{ 7.2 }[/math] [math]\displaystyle{ x^5 }[/math] [math]\displaystyle{ Gold }[/math] Gold 3708 198
[math]\displaystyle{ 7.3 }[/math] [math]\displaystyle{ x^9 }[/math] [math]\displaystyle{ Gold }[/math] Gold 3610 198
[math]\displaystyle{ 7.4 }[/math] [math]\displaystyle{ x^{13} }[/math] [math]\displaystyle{ Kasami }[/math] Gold 4270 338
[math]\displaystyle{ 7.5 }[/math] [math]\displaystyle{ x^{57} }[/math] [math]\displaystyle{ Kasami }[/math] Gold 4704 436
[math]\displaystyle{ 7.6 }[/math] [math]\displaystyle{ x^{63} }[/math] [math]\displaystyle{ Inverse }[/math] Inverse 8128 4928
[math]\displaystyle{ 7.7 }[/math] [math]\displaystyle{ x^3+Tr_7(x^9) }[/math] [math]\displaystyle{ C4 }[/math] Gold 4026 212
[math]\displaystyle{ 8 }[/math] [math]\displaystyle{ 8.1 }[/math] [math]\displaystyle{ x^3 }[/math] [math]\displaystyle{ Gold }[/math] Gold 11818 420
[math]\displaystyle{ 8.2 }[/math] [math]\displaystyle{ x^9 }[/math] [math]\displaystyle{ Gold }[/math] Gold 12370 420
[math]\displaystyle{ 8.3 }[/math] [math]\displaystyle{ x^{57} }[/math] [math]\displaystyle{ Kasami }[/math] Gold 15358 960
[math]\displaystyle{ 8.4 }[/math] [math]\displaystyle{ x^3+x^{17}+p^{48}x^{18}+p^3x^{33}+px^{34}+x^{48} }[/math] [math]\displaystyle{ C3 }[/math] Gold 13200 414
[math]\displaystyle{ 8.5 }[/math] [math]\displaystyle{ x^3+Tr_8(x^9) }[/math] [math]\displaystyle{ C4 }[/math] Gold 13200 432
[math]\displaystyle{ 8.6 }[/math] [math]\displaystyle{ x^3+a^{-1}Tr_8(a^3x^9) }[/math] [math]\displaystyle{ C4 }[/math] Gold 13842 436
[math]\displaystyle{ 8.7 }[/math] [math]\displaystyle{ a(x+x^{16})(ax+a^{16}x^{16})+a^{17}(ax+a^{16}x^{16})^{12} }[/math] [math]\displaystyle{ C10 }[/math] Gold 13642 436
[math]\displaystyle{ 9 }[/math] [math]\displaystyle{ 9.1 }[/math] [math]\displaystyle{ x^3 }[/math] [math]\displaystyle{ Gold }[/math] Gold 38470 872
[math]\displaystyle{ 9.2 }[/math] [math]\displaystyle{ x^5 }[/math] [math]\displaystyle{ Gold }[/math] Gold 41494 872
[math]\displaystyle{ 9.3 }[/math] [math]\displaystyle{ x^{17} }[/math] [math]\displaystyle{ Gold }[/math] Gold 38470 872
[math]\displaystyle{ 9.4 }[/math] [math]\displaystyle{ x^{13} }[/math] [math]\displaystyle{ Kasami }[/math] Gold 58676 3086
[math]\displaystyle{ 9.5 }[/math] [math]\displaystyle{ x^{241} }[/math] [math]\displaystyle{ Kasami }[/math] Gold 61726 3482
[math]\displaystyle{ 9.6 }[/math] [math]\displaystyle{ x^{19} }[/math] [math]\displaystyle{ Welch }[/math] Gold 60894 3956
[math]\displaystyle{ 9.7 }[/math] [math]\displaystyle{ x^{255} }[/math] [math]\displaystyle{ Inverse }[/math] Inverse 130816 93024
[math]\displaystyle{ 9.8 }[/math] [math]\displaystyle{ x^3+Tr_9(x^9) }[/math] [math]\displaystyle{ C4 }[/math] Gold 47890 920
[math]\displaystyle{ 9.9 }[/math] [math]\displaystyle{ x^3+Tr^3_9(x^9+x^{18}) }[/math] [math]\displaystyle{ C5 }[/math] Gold 48428 930
[math]\displaystyle{ 9.10 }[/math] [math]\displaystyle{ x^3+Tr^3_9(x^{18}+x^{36}) }[/math] [math]\displaystyle{ C6 }[/math] Gold 48460 944
[math]\displaystyle{ 9.11 }[/math] [math]\displaystyle{ x^3+a^{246}x^{10}+a^{47}x^{17}+a^{181}x^{66}+a^{428}x^{129} }[/math] [math]\displaystyle{ C11 }[/math] Gold 48596 944
[math]\displaystyle{ 10 }[/math] [math]\displaystyle{ 10.1 }[/math] [math]\displaystyle{ x^3 }[/math] [math]\displaystyle{ Gold }[/math] Gold 125042
[math]\displaystyle{ 10.2 }[/math] [math]\displaystyle{ x^9 }[/math] [math]\displaystyle{ Gold }[/math] Gold 136492
[math]\displaystyle{ 10.3 }[/math] [math]\displaystyle{ x^{57} }[/math] [math]\displaystyle{ Kasami }[/math] Gold 186416
[math]\displaystyle{ 10.4 }[/math] [math]\displaystyle{ x^{339} }[/math] [math]\displaystyle{ Dobbertin }[/math] Dobbertin 280604
[math]\displaystyle{ 10.5 }[/math] [math]\displaystyle{ x^6+x^{33}+p^{31}x^{192} }[/math] [math]\displaystyle{ C3 }[/math] Gold 151216
[math]\displaystyle{ 10.6 }[/math] [math]\displaystyle{ x^{33}+x^{72}+p^{31}x^{258} }[/math] [math]\displaystyle{ C3 }[/math] Gold 153896
[math]\displaystyle{ 10.7 }[/math] [math]\displaystyle{ x^3+Tr_{10}(x^9) }[/math] [math]\displaystyle{ C4 }[/math] Gold 164034
[math]\displaystyle{ 10.8 }[/math] [math]\displaystyle{ x^3+a^{-1}Tr_{10}(a^3x^9) }[/math] [math]\displaystyle{ C4 }[/math] Gold 164098
[math]\displaystyle{ 11 }[/math] [math]\displaystyle{ 11.1 }[/math] [math]\displaystyle{ x^3 }[/math] [math]\displaystyle{ Gold }[/math] Gold
[math]\displaystyle{ 11.2 }[/math] [math]\displaystyle{ x^5 }[/math] [math]\displaystyle{ Gold }[/math] Gold
[math]\displaystyle{ 11.3 }[/math] [math]\displaystyle{ x^9 }[/math] [math]\displaystyle{ Gold }[/math] Gold
[math]\displaystyle{ 11.4 }[/math] [math]\displaystyle{ x^{17} }[/math] [math]\displaystyle{ Gold }[/math] Gold
[math]\displaystyle{ 11.5 }[/math] [math]\displaystyle{ x^{33} }[/math] [math]\displaystyle{ Gold }[/math] Gold
[math]\displaystyle{ 11.6 }[/math] [math]\displaystyle{ x^{13} }[/math] [math]\displaystyle{ Kasami }[/math] Gold
[math]\displaystyle{ 11.7 }[/math] [math]\displaystyle{ x^{57} }[/math] [math]\displaystyle{ Kasami }[/math] Gold
[math]\displaystyle{ 11.8 }[/math] [math]\displaystyle{ x^{241} }[/math] [math]\displaystyle{ Kasami }[/math] Gold
[math]\displaystyle{ 11.9 }[/math] [math]\displaystyle{ x^{993} }[/math] [math]\displaystyle{ Kasami }[/math] Gold
[math]\displaystyle{ 11.10 }[/math] [math]\displaystyle{ x^{35} }[/math] [math]\displaystyle{ Welch }[/math] Gold
[math]\displaystyle{ 11.11 }[/math] [math]\displaystyle{ x^{287} }[/math] [math]\displaystyle{ Niho }[/math] Gold
[math]\displaystyle{ 11.12 }[/math] [math]\displaystyle{ x^{123} }[/math] [math]\displaystyle{ Inverse }[/math] Inverse
[math]\displaystyle{ 11.13 }[/math] [math]\displaystyle{ x^3+Tr_{11}(x^9) }[/math] [math]\displaystyle{ C4 }[/math] Gold