# Difference between revisions of "APN functions obtained via polynomial expansion in small dimensions"

ID Representative Equivalent to Orthoderivative diff. spec.
8.1 ${\displaystyle \alpha ^{170}x^{192}+\alpha ^{85}x^{132}+x^{6}+x^{3}}$ SW 19 ${\displaystyle 0^{37872},2^{22788},4^{4068},6^{492},8^{60}}$
8.2 ${\displaystyle x^{66}+\alpha ^{85}x^{33}+x^{18}+x^{9}+x^{3}}$ SW 11 ${\displaystyle 0^{38040},2^{22461},4^{4218},6^{513},8^{36},10^{12}}$
8.3 ${\displaystyle x^{66}+\alpha ^{85}x^{33}+\alpha ^{17}x^{9}+\alpha ^{102}x^{6}+x^{3}}$ SW 13 ${\displaystyle 0^{38076},2^{22311},4^{4374},6^{495},8^{24}}$
8.4 ${\displaystyle \alpha ^{85}x^{132}+\alpha ^{85}x^{72}+x^{9}+x^{6}+x^{3}}$ SW 12 ${\displaystyle 0^{38160},2^{22104},4^{4536},6^{456},8^{24}}$
8.5 ${\displaystyle x^{66}+x^{12}+\alpha ^{85}x^{6}+x^{3}}$ SW 6 ${\displaystyle 0^{38160},2^{22164},4^{4428},6^{492},8^{36}}$
8.6 ${\displaystyle x^{129}+\alpha ^{85}x^{24}+x^{12}+x^{9}+x^{3}}$ SW 8 ${\displaystyle 0^{38184},2^{22179},4^{4338},6^{531},8^{48}}$
8.7 ${\displaystyle \alpha ^{170}x^{132}+\alpha ^{85}x^{66}+\alpha ^{85}x^{18}+x^{3}}$ new ${\displaystyle 0^{38196},2^{22008},4^{4608},6^{456},8^{12}}$
8.8 ${\displaystyle \alpha ^{85}x^{132}+\alpha ^{85}x^{72}+x^{36}+x^{24}+x^{3}}$ SW 9 ${\displaystyle 0^{38256},2^{22116},4^{4230},6^{648},8^{30}}$
8.9 ${\displaystyle \alpha ^{85}x^{192}+x^{72}+x^{33}+x^{24}+x^{9}+\alpha ^{153}x^{6}}$ SW 17 ${\displaystyle 0^{38388},2^{21723},4^{4626},6^{507},8^{36}}$
8.10 ${\displaystyle \alpha ^{221}x^{96}+\alpha ^{221}x^{33}+x^{12}+x^{9}+x^{6}+\alpha ^{187}*x^{3}}$ SW 10 ${\displaystyle 0^{38439},2^{21618},4^{4671},6^{528},8^{24}}$
8.11 ${\displaystyle \alpha ^{238}x^{144}+x^{132}+\alpha ^{51}x^{96}+\alpha ^{119}x^{48}+x^{33}+x^{9}}$ SW 16 ${\displaystyle 0^{38457},2^{21552},4^{4743},6^{510},8^{18}}$
8.12 ${\displaystyle \alpha ^{204}x^{160}+\alpha ^{51}x^{48}+\alpha ^{102}x^{12}+\alpha ^{204}x^{10}+x^{9}}$ SW 22 ${\displaystyle 0^{38844},2^{20974},4^{4764},6^{654},8^{44}}$
8.13 ${\displaystyle \alpha ^{160}x^{132}+\alpha ^{10}x^{72}+x^{48}+\alpha x^{34}+\alpha ^{3}x^{33}+\alpha ^{48}x^{18}+x^{17}+x^{3}}$ B 31 ${\displaystyle 0^{39150},2^{20463},4^{4920},6^{675},8^{54},10^{12},12^{6}}$
8.14 ${\displaystyle x^{144}+\alpha ^{85}x^{96}+\alpha ^{170}x^{80}+\alpha ^{85}x^{65}+\alpha ^{85}x^{17}+x^{9}+x^{5}}$ B 12668 ${\displaystyle 0^{39408},2^{20072},4^{4922},6^{798},8^{70},10^{10}}$
8.15 ${\displaystyle x^{66}+\alpha ^{170}x^{40}+x^{18}+\alpha ^{85}x^{5}+x^{3}}$ Y 4346 ${\displaystyle 0^{39408},2^{20218},4^{4692},6^{838},8^{104},10^{12},12^{8}}$
8.16 ${\displaystyle x^{160}+x^{132}+x^{80}+x^{68}+x^{6}+x^{3}}$ SW 20 ${\displaystyle 0^{39692},2^{19752},4^{4756},6^{978},8^{72},10^{26},12^{4}}$
ID Representative Equivalent to Orthoderivative diff. spec.
9.1 ${\displaystyle \alpha ^{365}x^{257}+x^{96}+x^{68}+\alpha ^{219}x^{33}+x^{5}}$ I 4 ${\displaystyle 0^{158529},2^{80829},4^{18144},6^{3283},8^{469},10^{294},12^{84}}$
9.2 ${\displaystyle \alpha ^{438}x^{129}+x^{66}+\alpha ^{219}x^{10}+x^{3}}$ I 8 ${\displaystyle 0^{159418},2^{79275},4^{18690},6^{3213},8^{742},10^{252},12^{21},16^{21}}$
9.3 ${\displaystyle x^{136}+x^{24}+x^{17}+\alpha ^{73}x^{10}+x^{3}}$ I 3 ${\displaystyle 0^{159684},2^{78687},4^{19089},6^{3136},8^{777},10^{147},12^{84},14^{28}}$
9.4 ${\displaystyle x^{68}+\alpha ^{73}x^{40}+x^{33}+x^{5}}$ I 10 ${\displaystyle 0^{159684},2^{79590},4^{17871},6^{3283},8^{700},10^{273},12^{147},14^{84}}$
9.5 ${\displaystyle \alpha ^{73}x^{136}+\alpha ^{146}x^{66}+\alpha ^{219}x^{10}+x^{3}}$ I 16 ${\displaystyle 0^{159908},2^{79086},4^{18081},6^{3353},8^{721},10^{336},12^{105},14^{21},16^{21}}$
9.6 ${\displaystyle x^{264}+\alpha ^{73}x^{96}+\alpha ^{219}x^{68}+x^{5}}$ I 11 ${\displaystyle 0^{160020},2^{79023},4^{17997},6^{3213},8^{868},10^{378},12^{133}}$
9.7 ${\displaystyle \alpha ^{219}x^{136}+x^{10}+x^{3}}$ I 12 ${\displaystyle 0^{160657},2^{77910},4^{18312},6^{3360},8^{952},10^{273},12^{147},14^{21}}$
9.8 ${\displaystyle x^{192}+x^{66}+x^{17}+\alpha ^{73}x^{10}+x^{3}}$ I 14 ${\displaystyle 0^{162183},2^{76482},4^{17388},6^{3871},8^{1162},10^{252},12^{126},14^{126},16^{21},22^{21}}$
9.9 ${\displaystyle \alpha ^{73}x^{192}+x^{136}+\alpha ^{365}x^{129}+x^{17}+x^{3}}$ I 5 ${\displaystyle 0^{162708},2^{77175},4^{15498},6^{4270},8^{1260},10^{252},12^{168},14^{84},16^{126},18^{42},22^{42},26^{7}}$
9.10 ${\displaystyle \alpha ^{73}x^{129}+\alpha ^{292}x^{66}+x^{10}+x^{3}}$ I 9 ${\displaystyle 0^{163009},2^{75537},4^{17283},6^{4116},8^{1071},10^{168},12^{231},14^{28},16^{84},18^{63},20^{42}}$
9.11 ${\displaystyle x^{80}+\alpha ^{146}x^{66}+\alpha ^{73}x^{24}+x^{17}}$ I 13 ${\displaystyle 0^{163366},2^{75117},4^{17010},6^{4536},8^{966},10^{252},12^{63},14^{154},16^{63},18^{84},22^{21}}$
9.12 ${\displaystyle x^{129}+\alpha ^{73}x^{66}+x^{17}+x^{10}+\alpha ^{365}x^{3}}$ I 6 ${\displaystyle 0^{163996},2^{74802},4^{16380},6^{4368},8^{1449},10^{231},12^{126},14^{84},16^{42},18^{84},20^{42},22^{21},32^{7}}$
9.13 ${\displaystyle \alpha ^{73}x^{136}+\alpha ^{219}x^{66}+\alpha ^{438}x^{10}+x^{3}}$ I 15 ${\displaystyle 0^{168994},2^{68712},4^{15141},6^{6279},8^{1659},10^{336},12^{21},14^{21},16^{105},18^{147},20^{189},24^{21},26^{7}}$
9.14 ${\displaystyle \alpha ^{438}x^{129}+x^{66}+\alpha ^{219}x^{17}+x^{3}}$ I 2 ${\displaystyle 0^{169428},2^{68040},4^{15561},6^{6034},8^{1533},10^{420},12^{126},14^{21},16^{84},18^{189},20^{126},22^{63},26^{7}}$
9.15 ${\displaystyle \alpha ^{365}x^{80}+\alpha ^{292}x^{24}+\alpha ^{219}x^{17}+x^{3}}$ I 17 ${\displaystyle 0^{170079},2^{66297},4^{16737},6^{6160},8^{1407},10^{420},12^{21},14^{42},16^{63},18^{210},20^{133},22^{63}}$
9.16 ${\displaystyle x^{257}+\alpha ^{438}x^{68}+\alpha ^{219}x^{12}+x^{5}}$ I 7 ${\displaystyle 0^{171430},2^{64617},4^{16842},6^{5733},8^{1932},10^{483},12^{105},14^{21},16^{147},18^{105},20^{154},22^{21},24^{42}}$
9.17 ${\displaystyle x^{80}+\alpha ^{73}x^{66}+x^{17}+\alpha ^{73}x^{10}+x^{3}}$ B 31 ${\displaystyle 0^{160440},2^{78834},4^{17514},6^{3388},8^{777},10^{483},12^{126},14^{49},16^{21}}$
9.18 ${\displaystyle \alpha ^{365}x^{136}+x^{129}+\alpha ^{73}x^{80}+x^{24}+x^{17}+x^{3}}$ B 34 ${\displaystyle 0^{164199},2^{76734},4^{13524},6^{4312},8^{2205},12^{147},16^{294},18^{147},20^{49},22^{21}}$
9.19 ${\displaystyle \alpha ^{73}x^{320}+x^{96}+\alpha ^{219}x^{68}+x^{40}+x^{33}+x^{5}}$ B 35 ${\displaystyle 0^{172557},2^{68355},4^{12201},6^{3871},8^{1638},10^{735},12^{1470},14^{49},16^{147},18^{441},20^{147},42^{21}}$