APN functions obtained via polynomial expansion in small dimensions: Difference between revisions

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<td>SW 20</td>
<td>SW 20</td>
<td><math>0^{39692}, 2^{19752}, 4^{4756}, 6^{978}, 8^{72}, 10^{26}, 12^4</math></td>
<td><math>0^{39692}, 2^{19752}, 4^{4756}, 6^{978}, 8^{72}, 10^{26}, 12^4</math></td>
</tr>
</table>
<table>
<th>ID</th>
<th>Representative</th>
<th>Equivalent to</th>
<th>Orthoderivative diff. spec.</th>
</tr>
<tr>
<td>9.1</td>
<td><math>\alpha^{365}x^{257} + x^{96} + x^{68} + \alpha^{219}x^{33} + x^5</math></td>
<td>I 4</td>
<td><math>0^{158529}, 2^{80829}, 4^{18144}, 6^{3283}, 8^{469}, 10^{294}, 12^{84}</math></td>
</tr>
<tr>
<td>9.2</td>
<td><math>\alpha^{438}x^{129} + x^{66} + \alpha^{219}x^{10} + x^3</math></td>
<td>I 8</td>
<td><math>0^{159418}, 2^{79275}, 4^{18690}, 6^{3213}, 8^{742}, 10^{252}, 12^{21}, 16^{21}</math></td>
</tr>
<tr>
<td>9.3</td>
<td><math>x^{136} + x^{24} + x^{17} + \alpha^{73}x^{10} + x^3</math></td>
<td>I 3</td>
<td><math>0^{159684}, 2^{78687}, 4^{19089}, 6^{3136}, 8^{777}, 10^{147}, 12^{84}, 14^{28}</math></td>
</tr>
<tr>
<td>9.4</td>
<td><math>x^{68} + \alpha^{73}x^{40} + x^{33} + x^5</math></td>
<td>I 10</td>
<td><math>0^{159684}, 2^{79590}, 4^{17871}, 6^{3283}, 8^{700}, 10^{273}, 12^{147}, 14^{84}</math></td>
</tr>
<tr>
<td>9.5</td>
<td><math>\alpha^{73}x^{136} + \alpha^{146}x^{66} + \alpha^{219}x^{10} + x^3</math></td>
<td>I 16</td>
<td><math>0^{159908}, 2^{79086}, 4^{18081}, 6^{3353}, 8^{721}, 10^{336}, 12^{105}, 14^{21}, 16^{21}</math></td>
</tr>
<tr>
<td>9.6</td>
<td><math>x^{264} + \alpha^{73}x^{96} + \alpha^{219}x^{68} + x^5</math></td>
<td>I 11</td>
<td><math>0^{160020}, 2^{79023}, 4^{17997}, 6^{3213}, 8^{868}, 10^{378}, 12^{133}</math></td>
</tr>
<tr>
<td>9.7</td>
<td><math>\alpha^{219}x^{136} + x^{10} + x^3</math></td>
<td>I 12</td>
<td><math>0^{160657}, 2^{77910}, 4^{18312}, 6^{3360}, 8^{952}, 10^{273}, 12^{147}, 14^{21}</math></td>
</tr>
<tr>
<td>9.8</td>
<td><math>x^{192} + x^{66} + x^{17} + \alpha^{73}x^{10} + x^3</math></td>
<td>I 14</td>
<td><math>0^{162183}, 2^{76482}, 4^{17388}, 6^{3871}, 8^{1162}, 10^{252}, 12^{126}, 14^{126}, 16^{21}, 22^{21}</math></td>
</tr>
<tr>
<td>9.9</td>
<td><math>\alpha^{73}x^{192} + x^{136} + \alpha^{365}x^{129} + x^{17} + x^3</math></td>
<td>I 5</td>
<td><math>0^{162708}, 2^{77175}, 4^{15498}, 6^{4270}, 8^{1260}, 10^{252}, 12^{168}, 14^{84}, 16^{126}, 18^{42}, 22^{42}, 26^7</math></td>
</tr>
<tr>
<td>9.10</td>
<td><math>\alpha^{73}x^{129} + \alpha^{292}x^{66} + x^{10} + x^3</math></td>
<td>I 9</td>
<td><math>0^{163009}, 2^{75537}, 4^{17283}, 6^{4116}, 8^{1071}, 10^{168}, 12^{231}, 14^{28}, 16^{84}, 18^{63}, 20^{42}</math></td>
</tr>
<tr>
<td>9.11</td>
<td><math>x^{80} + \alpha^{146}x^{66} + \alpha^{73}x^{24} + x^{17}</math></td>
<td>I 13</td>
<td><math>0^{163366}, 2^{75117}, 4^{17010}, 6^{4536}, 8^{966}, 10^{252}, 12^{63}, 14^{154}, 16^{63}, 18^{84}, 22^{21}</math></td>
</tr>
<tr>
<td>9.12</td>
<td><math>x^{129} + \alpha^{73}x^{66} + x^{17} + x^{10} + \alpha^{365}x^3</math></td>
<td>I 6</td>
<td><math>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</math></td>
</tr>
<tr>
<td>9.13</td>
<td><math>\alpha^{73}x^{136} + \alpha^{219}x^{66} + \alpha^{438}x^{10} + x^3</math></td>
<td>I 15</td>
<td><math>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</math></td>
</tr>
<tr>
<td>9.14</td>
<td><math>\alpha^{438}x^{129} + x^{66} + \alpha^{219}x^{17} + x^3</math></td>
<td>I 2</td>
<td><math>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</math></td>
</tr>
<tr>
<td>9.15</td>
<td><math>\alpha^{365}x^{80} + \alpha^{292}x^{24} + \alpha^{219}x^{17} + x^3</math></td>
<td>I 17</td>
<td><math>0^{170079}, 2^{66297}, 4^{16737}, 6^{6160}, 8^{1407}, 10^{420}, 12^{21}, 14^{42}, 16^{63}, 18^{210}, 20^{133}, 22^{63}</math></td>
</tr>
<tr>
<td>9.16</td>
<td><math>x^{257} + \alpha^{438}x^{68} + \alpha^{219}x^{12} + x^5</math></td>
<td>I 7</td>
<td><math>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}</math></td>
</tr>
<tr>
<td>9.17</td>
<td><math>x^{80} + \alpha^{73}x^{66} + x^{17} + \alpha^{73}x^{10} + x^3</math></td>
<td>B 31</td>
<td><math>0^{160440}, 2^{78834}, 4^{17514}, 6^{3388}, 8^{777}, 10^{483}, 12^{126}, 14^{49}, 16^{21}</math></td>
</tr>
<tr>
<td>9.18</td>
<td><math>\alpha^{365}x^{136} + x^{129} + \alpha^{73}x^{80} + x^{24} + x^{17} + x^3</math></td>
<td>B 34</td>
<td><math>0^{164199}, 2^{76734}, 4^{13524}, 6^{4312}, 8^{2205}, 12^{147}, 16^{294}, 18^{147}, 20^{49}, 22^{21}</math></td>
</tr>
<tr>
<td>9.19</td>
<td><math>\alpha^{73}x^{320} + x^{96} + \alpha^{219}x^{68} + x^{40} + x^{33} + x^5</math></td>
<td>B 35</td>
<td><math>0^{172557}, 2^{68355}, 4^{12201}, 6^{3871}, 8^{1638}, 10^{735}, 12^{1470}, 14^{49}, 16^{147}, 18^{441}, 20^{147}, 42^{21}</math></td>
</tr>
</tr>
</table>
</table>

Revision as of 17:42, 1 September 2021

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