APN functions obtained via polynomial expansion in small dimensions: Difference between revisions
Jump to navigation
Jump to search
(Created page with "<table> <tr> <th>ID</th> <th>Representative</th> <th>Equivalent to</th> <th>Orthoderivative diff. spec.</th> </tr> <tr> <td>8.1</td> <td><math>\alpha^{170}x^{192} + \alpha^{85...") |
No edit summary |
||
Line 100: | Line 100: | ||
<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] |