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

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families) in Small Dimensions with Coefficients as 1
families) in Small Dimensions with Coefficients as 1


<table>
 
<table class="borderless">
<tr>
<tr>
<th><math>n</math></th>
<th><math>n</math></th>
Line 190: Line 191:
</tr>
</tr>


<tr>
<tr class="divider">
<td><math>7</math></td>
<td rowspan="10"><math>7</math></td>
<td><math>7.1</math>
<td class="noborderbelow"><math>7.1</math></td>
<td><math>x^{68} + x^{40} + x^{24} + x^6 + x^3</math></td>
<td><math>-</math></td>
<td><math>Table 7: N^\circ13.1</math></td>
</tr>


<math>7.2</math>
<td><math>7.2</math></td>
<td><math>x^{65} + x^{20} + x^{18} + x^6 + x^3</math></td>
<td><math>N^\circ5</math></td>
<td><math>7:N^\circ1.2</math></td>
</tr>


<math>7.3</math>
<td><math>7.3</math></td>
<td><math>x^{40} + x^{34} + x^{18} + x^{10} + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ12.1</math></td>
</tr>


<math>7.4</math>
<td><math>7.4</math></td>
<td><math>x^{48} + x^{40} + x^{10} + x^9 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ2.1</math></td>
</tr>


<math>7.5</math>
<td><math>7.5</math></td>
<td><math>x^{33} + x^9 + x^6 + x^5 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ11.1</math></td>
</tr>


<math>7.6</math>
<td><math>7.6</math></td>
<td><math>x^{40} + x^{36} + x^{34} + x^{24} + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ10.1</math></td>
</tr>


<math>7.7</math>
<td><math>7.7</math></td>
<td><math>x^{24} + x^{10} + x^9 + x^6 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ2.1</math></td>
</tr>


<math>7.8</math>
<td><math>7.8</math></td>
<td><math>x^{65} + x^{36} + x^{20} + x^{17} + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ14.1</math></td>
</tr>


<math>7.9</math>
<td><math>7.9</math></td>
<td><math>x^{40} + x^{33} + x^{17} + x^5 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ8.1</math></td>
</tr>


<math>7.10</math></td>
<td><math>7.10</math></td>
<td><math>x^{36} + x^{33} + x^{18} + x^9 + x^5</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ10.1</math></td>
</tr>


<tr class="divider">
<td rowspan="4"><math>8</math></td>
<td class="noborderbelow"><math>8.1</math></td>
<td><math>x^{36} + x^{33} + x^9 + x^6 + x^3</math></td>
<td><math>-</math></td>
<td><math>Table 9: N^\circ1.4</math></td>
</tr>


<td><math>x^{68} + x^{40} + x^{24} + x^6 + x^3</math>
<td><math>8.2</math></td>
<td><math>x^{72} + x^{66} + x^{12} + x^6 + x^3</math></td>
<td><math>N^\circ5</math></td>
<td><math>9:N^\circ1.3</math></td>
</tr>


<math>x^{65} + x^{20} + x^{18} + x^6 + x^3</math>
<td><math>8.3</math></td>
 
<td><math>x^{130} + x^{66} + x^{40} + x^{12} + x^3</math></td>
<math>x^{40} + x^{34} + x^{18} + x^{10} + x^3</math>
<td><math>-</math></td>
 
<td><math>9:N^\circ6.1</math></td>
<math>x^{48} + x^{40} + x^{10} + x^9 + x^3</math>
 
<math>x^{33} + x^9 + x^6 + x^5 + x^3</math>
 
<math>x^{40} + x^{36} + x^{34} + x^{24} + x^3</math>
 
<math>x^{24} + x^{10} + x^9 + x^6 + x^3</math>
 
<math>x^{65} + x^{36} + x^{20} + x^{17} + x^3</math>
 
<math>x^{40} + x^{33} + x^{17} + x^5 + x^3</math>
 
<math>x^{36} + x^{33} + x^{18} + x^9 + x^5</math></td>
 
<td><math>-</math>
 
<math>N^\circ5</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math></td>
 
<td><math>Table 7: N^\circ13.1</math>
 
<math>7:N^\circ1.2</math>
 
<math>7:N^\circ12.1</math>
 
<math>7:N^\circ2.1</math>
 
<math>7:N^\circ11.1</math>
 
<math>7:N^\circ10.1</math>
 
<math>7:N^\circ2.1</math>
 
<math>7:N^\circ14.1</math>
 
<math>7:N^\circ8.1</math>
 
<math>7:N^\circ10.1</math></td>
</tr>
</tr>


 
<td><math>8.4</math></td>
<tr>
<td><math>x^{66} + x^{40} + x^{18} + x^5 + x^3</math></td>
<td><math>8</math></td>
<td><math>-</math></td>
 
<td><math>9:N^\circ5.1</math></td>
<td><math>8.1</math>
 
<math>8.2</math>
 
<math>8.3</math>
 
<math>8.4</math></td>
 
 
<td><math>x^{36} + x^{33} + x^9 + x^6 + x^3</math>
 
<math>x^{72} + x^{66} + x^{12} + x^6 + x^3</math>
 
<math>x^{130} + x^{66} + x^{40} + x^{12} + x^3</math>
 
<math>x^{66} + x^{40} + x^{18} + x^5 + x^3</math></td>
 
<td><math>-</math>
 
<math>N^\circ5</math>
 
<math>-</math>
 
<math>-</math></td>
 
<td><math>Table 9: N^\circ1.4</math>
 
<math>9:N^\circ1.3</math>
 
<math>9:N^\circ6.1</math>
 
<math>9:N^\circ5.1</math></td>
</tr>
</tr>


<tr>
<tr class="divider">
<td><math>9</math></td>
<td><math>9</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
Line 320: Line 287:
</tr>
</tr>


 
<tr class="divider">
<tr>
<td><math>10</math></td>
<td><math>10</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
Line 329: Line 295:
</tr>
</tr>


<tr class="divider">
<td rowspan="5"><math>11</math></td>
<td class="noborderbelow"><math>11.1</math></td>
<td><math>x^{12} + x^{10} + x^9 + x^5 + x^3</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>


<tr>
<td><math>11.2</math></td>
<td><math>11</math></td>
<td><math>x^{258} + x^{257} + x^{18} + x^{17} + x^3</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>


<td><math>11.1</math>
<td><math>11.3</math></td>
<td><math>x^{96} + x^{66} + x^{34} + x^{33} + x^3</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>


<math>11.2</math>
<td><math>11.4</math></td>
 
<td><math>x^{80} + x^{68} + x^{65} + x^{17} + x^5</math></td>
<math>11.3</math>
<td><math>-</math></td>
 
<td><math>-</math></td>
<math>11.4</math>
</tr>
 
<math>11.5</math></td>
 
 
<td><math>x^{12} + x^{10} + x^9 + x^5 + x^3</math>
 
<math>x^{258} + x^{257} + x^{18} + x^{17} + x^3</math>
 
<math>x^{96} + x^{66} + x^{34} + x^{33} + x^3</math>
 
<math>x^{80} + x^{68} + x^{65} + x^{17} + x^5</math>
 
<math>x^{260} + x^{257} + x^{36} + x^{33} + x^5</math></td>
 
 
<td><math>-</math>
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math></td>
 
<td><math>-</math>
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math></td>


<td><math>11.5</math></td>
<td><math>x^{260} + x^{257} + x^{36} + x^{33} + x^5</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>
</tr>


Line 382: Line 334:


<table>
<table>
<table class="borderless">
<tr>
<tr>
<th><math>n</math></th>
<th><math>n</math></th>
Line 398: Line 351:
</tr>
</tr>


<tr>
<tr class="divider">
<td><math>7</math></td>
<td rowspan="12"><math>7</math></td>
<td><math>7.1</math>
<td class="noborderbelow"><math>7.1</math></td>
<td><math>x^{34} + x^{33} + x^{12} + x^6 + x^5 + x^3</math></td>
<td><math>-</math></td>
<td><math>Table 7: N^\circ14.2</math></td>
</tr>


<math>7.2</math>
<td><math>7.2</math></td>
<td><math>x^{40} + x^{24} + x^{20} + x^9 + x^5 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ14.1</math></td>
</tr>


<math>7.3</math>
<td><math>7.3</math></td>
<td><math>x^{33} + x^{24} + x^{20} + x^{18} + x^{12} + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ12.1</math></td>
</tr>


<math>7.4</math>
<td><math>7.4</math></td>
<td><math>x^{24} + x^{17} + x^{12} + x^{10} + x^6 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ2.1</math></td>
</tr>


<math>7.5</math>
<td><math>7.5</math></td>
<td><math>x^{40} + x^{34} + x^{18} + x^{17} + x^5 + x^3</math></td>
<td><math>N^\circ5</math></td>
<td><math>7:N^\circ1.2</math></td>
</tr>


<math>7.6</math>
<td><math>7.6</math></td>
<td><math>x^{48} + x^{40} + x^{18} + x^{10} + x^5 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ11.1</math></td>
</tr>


<math>7.7</math>
<td><math>7.7</math></td>
<td><math>x^{40} + x^{12} + x^{10} + x^9 + x^5 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ2.2</math></td>
</tr>


<math>7.8</math>
<td><math>7.8</math></td>
<td><math>x^{34} + x^{24} + x^{10} + x^9 + x^6 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ9.1</math></td>
</tr>


<math>7.9</math>
<td><math>7.9</math></td>
<td><math>x^{34} + x^{33} + x^{20} + x^{17} + x^{10} + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ13.1</math></td>
</tr>


<math>7.10</math>
<td><math>7.10</math></td>
<td><math>x^{36} + x^{33} + x^{24} + x^9 + x^6 + x^3</math>
<td><math>-</math></td>
<td><math>7:N^\circ10.1</math></td>
</tr>


<math>7.11</math>
<td><math>7.11</math></td>
<td><math>x^{40} + x^{36} + x^{20} + x^{10} + x^5 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ10.2</math></td>
</tr>


<math>7.12</math></td>
<td><math>7.12</math></td>
<td><math>x^{36} + x^{34} + x^{20} + x^{10} + x^9 + x^3</math></td>
<td><math>-</math></td>
<td><math>7:N^\circ8.1</math></td>
</tr>


<tr class="divider">
<td rowspan="3"><math>8</math></td>
<td class="noborderbelow"><math>8.1</math></td>
<td><math>x^{68} + x^{34} + x^{17} + x^{12} + x^9 + x^3</math></td>
<td><math>-</math></td>
<td><math>Table 9: N^\circ5.1</math></td>
</tr>


<td><math>x^{34} + x^{33} + x^{12} + x^6 + x^5 + x^3</math>
<td><math>8.2</math></td>
 
<td><math>x^{72} + x^{40} + x^{34} + x^{20} + x^{12} + x^3</math></td>
<math>x^{40} + x^{24} + x^{20} + x^9 + x^5 + x^3</math>
<td><math>N^\circ5</math></td>
 
<td><math>9:N^\circ6.1</math></td>
<math>x^{33} + x^{24} + x^{20} + x^{18} + x^{12} + x^3</math>
 
<math>x^{24} + x^{17} + x^{12} + x^{10} + x^6 + x^3</math>
 
<math>x^{40} + x^{34} + x^{18} + x^{17} + x^5 + x^3</math>
 
<math>x^{48} + x^{40} + x^{18} + x^{10} + x^5 + x^3</math>
 
<math>x^{40} + x^{12} + x^{10} + x^9 + x^5 + x^3</math>
 
<math>x^{34} + x^{24} + x^{10} + x^9 + x^6 + x^3</math>
 
<math>x^{34} + x^{33} + x^{20} + x^{17} + x^{10} + x^3</math>
 
<math>x^{36} + x^{33} + x^{24} + x^9 + x^6 + x^3</math>
 
<math>x^{40} + x^{36} + x^{20} + x^{10} + x^5 + x^3</math>
 
<math>x^{36} + x^{34} + x^{20} + x^{10} + x^9 + x^3</math></td>
 
<td><math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>N^\circ5</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math>
 
<math>-</math></td>
 
<td><math>Table 7: N^\circ14.2</math>
 
<math>7:N^\circ14.1</math>
 
<math>7:N^\circ12.1</math>
 
<math>7:N^\circ2.1</math>
 
<math>7:N^\circ1.2</math>
 
<math>7:N^\circ11.1</math>
 
<math>7:N^\circ2.2</math>
 
<math>7:N^\circ9.1</math>
 
<math>7:N^\circ13.1</math>
 
<math>7:N^\circ10.1</math>
 
<math>7:N^\circ10.2</math>
 
<math>7:N^\circ8.1</math></td>
</tr>
</tr>


 
<td><math>8.3</math></td>
<tr>
<td><math>x^{72} + x^{66} + x^{34} + x^{18} + x^{10} + x^5</math></td></td>
<td><math>8</math></td>
<td><math>-</math></td>
 
<td><math>9:N^\circ4.1</math></td>
<td><math>8.1</math>
 
<math>8.2</math>
 
<math>8.3</math></td>
 
 
<td><math>x^{68} + x^{34} + x^{17} + x^{12} + x^9 + x^3</math>
 
<math>x^{72} + x^{40} + x^{34} + x^{20} + x^{12} + x^3</math>
 
<math>x^{72} + x^{66} + x^{34} + x^{18} + x^{10} + x^5</math></td>
 
<td><math>-</math>
 
<math>N^\circ5</math>
 
<math>-</math>
 
<math>-</math></td>
 
<td><math>Table 9: N^\circ5.1</math>
 
<math>9:N^\circ6.1</math>
 
<math>9:N^\circ4.1</math></td>
 
</tr>
</tr>


<tr>
<tr class="divider">
<td><math>9</math></td>
<td><math>9</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
Line 539: Line 453:
</tr>
</tr>


 
<tr class="divider">
<tr>
<td><math>10</math></td>
<td><math>10</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
Line 548: Line 461:
</tr>
</tr>


 
<tr class="divider">
<tr>
<td><math>11</math></td>
<td><math>11</math></td>
<td><math>-</math></td>
<td><math>-</math></td>

Revision as of 12:55, 21 February 2019

Table 1: Classification of Quadratic APN Trinomials (CCZ-inequivalent to infinite monomial families) in Small Dimensions with Coefficients in [math]\displaystyle{ \mathbb{F}_2 }[/math]

[math]\displaystyle{ n }[/math] [math]\displaystyle{ N^\circ }[/math] Functions Families from tables 5 Relation to [6]
[math]\displaystyle{ 6 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 7 }[/math] [math]\displaystyle{ 7.1 }[/math] [math]\displaystyle{ x^{20} + x^6 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ Table 7: N^\circ 8.1 }[/math]
[math]\displaystyle{ 7.2 }[/math] [math]\displaystyle{ x^{34} + x^{18} + x^5 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7: N^\circ 2.1 }[/math]
[math]\displaystyle{ 8 }[/math] [math]\displaystyle{ 8.1 }[/math] [math]\displaystyle{ x^{72} + x^6 + x^3 }[/math] [math]\displaystyle{ N^\circ5 }[/math] [math]\displaystyle{ Table 9: N^\circ1.3 }[/math]
[math]\displaystyle{ 8.2 }[/math] [math]\displaystyle{ x^{72} + x^{36} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 9:N^\circ1.4 }[/math]
[math]\displaystyle{ 9 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 10 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 11 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]


Table 2: Classification of Quadratic APN Quadrinomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with Coefficients as 1

[math]\displaystyle{ n }[/math] [math]\displaystyle{ N^\circ }[/math] Functions Families from tables 5 Relation to [6]
[math]\displaystyle{ 6 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 7 }[/math] [math]\displaystyle{ 7.1 }[/math] [math]\displaystyle{ x^{72} + x^{40} + x^{12} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ Table 7: N^\circ12.1 }[/math]
[math]\displaystyle{ 7.2 }[/math] [math]\displaystyle{ x^{33} + x^{17} + x^{12} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ2.2 }[/math]
[math]\displaystyle{ 7.3 }[/math] [math]\displaystyle{ x^{34} + x^{33} + x^{10} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ10.1 }[/math]
[math]\displaystyle{ 7.4 }[/math] [math]\displaystyle{ x^{66} + x^{34} + x^{20} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ11.1 }[/math]
[math]\displaystyle{ 7.5 }[/math] [math]\displaystyle{ x^{68} + x^{18} + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ8.1 }[/math]
[math]\displaystyle{ 7.6 }[/math] [math]\displaystyle{ x^{66} + x^{18} + x^9 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ9.1 }[/math]
[math]\displaystyle{ 8 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 9 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 10 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 11 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]


Table 3: Classification of Quadratic APN Quadrinomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with Coefficients as 1


[math]\displaystyle{ n }[/math] [math]\displaystyle{ N^\circ }[/math] Functions Families from tables 5 Relation to [6]
[math]\displaystyle{ 6 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 7 }[/math] [math]\displaystyle{ 7.1 }[/math] [math]\displaystyle{ x^{68} + x^{40} + x^{24} + x^6 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ Table 7: N^\circ13.1 }[/math]
[math]\displaystyle{ 7.2 }[/math] [math]\displaystyle{ x^{65} + x^{20} + x^{18} + x^6 + x^3 }[/math] [math]\displaystyle{ N^\circ5 }[/math] [math]\displaystyle{ 7:N^\circ1.2 }[/math]
[math]\displaystyle{ 7.3 }[/math] [math]\displaystyle{ x^{40} + x^{34} + x^{18} + x^{10} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ12.1 }[/math]
[math]\displaystyle{ 7.4 }[/math] [math]\displaystyle{ x^{48} + x^{40} + x^{10} + x^9 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ2.1 }[/math]
[math]\displaystyle{ 7.5 }[/math] [math]\displaystyle{ x^{33} + x^9 + x^6 + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ11.1 }[/math]
[math]\displaystyle{ 7.6 }[/math] [math]\displaystyle{ x^{40} + x^{36} + x^{34} + x^{24} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ10.1 }[/math]
[math]\displaystyle{ 7.7 }[/math] [math]\displaystyle{ x^{24} + x^{10} + x^9 + x^6 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ2.1 }[/math]
[math]\displaystyle{ 7.8 }[/math] [math]\displaystyle{ x^{65} + x^{36} + x^{20} + x^{17} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ14.1 }[/math]
[math]\displaystyle{ 7.9 }[/math] [math]\displaystyle{ x^{40} + x^{33} + x^{17} + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ8.1 }[/math]
[math]\displaystyle{ 7.10 }[/math] [math]\displaystyle{ x^{36} + x^{33} + x^{18} + x^9 + x^5 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ10.1 }[/math]
[math]\displaystyle{ 8 }[/math] [math]\displaystyle{ 8.1 }[/math] [math]\displaystyle{ x^{36} + x^{33} + x^9 + x^6 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ Table 9: N^\circ1.4 }[/math]
[math]\displaystyle{ 8.2 }[/math] [math]\displaystyle{ x^{72} + x^{66} + x^{12} + x^6 + x^3 }[/math] [math]\displaystyle{ N^\circ5 }[/math] [math]\displaystyle{ 9:N^\circ1.3 }[/math]
[math]\displaystyle{ 8.3 }[/math] [math]\displaystyle{ x^{130} + x^{66} + x^{40} + x^{12} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 9:N^\circ6.1 }[/math]
[math]\displaystyle{ 8.4 }[/math] [math]\displaystyle{ x^{66} + x^{40} + x^{18} + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 9:N^\circ5.1 }[/math]
[math]\displaystyle{ 9 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 10 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 11 }[/math] [math]\displaystyle{ 11.1 }[/math] [math]\displaystyle{ x^{12} + x^{10} + x^9 + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 11.2 }[/math] [math]\displaystyle{ x^{258} + x^{257} + x^{18} + x^{17} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 11.3 }[/math] [math]\displaystyle{ x^{96} + x^{66} + x^{34} + x^{33} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 11.4 }[/math] [math]\displaystyle{ x^{80} + x^{68} + x^{65} + x^{17} + x^5 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 11.5 }[/math] [math]\displaystyle{ x^{260} + x^{257} + x^{36} + x^{33} + x^5 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]


Table 4: Classification of Quadratic APN Hexanomial (CCZ-inequivalent with infinite monomial families) in Small Dimensions with Coefficients as 1

[math]\displaystyle{ n }[/math] [math]\displaystyle{ N^\circ }[/math] Functions Families from tables 5 Relation to [6]
[math]\displaystyle{ 6 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 7 }[/math] [math]\displaystyle{ 7.1 }[/math] [math]\displaystyle{ x^{34} + x^{33} + x^{12} + x^6 + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ Table 7: N^\circ14.2 }[/math]
[math]\displaystyle{ 7.2 }[/math] [math]\displaystyle{ x^{40} + x^{24} + x^{20} + x^9 + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ14.1 }[/math]
[math]\displaystyle{ 7.3 }[/math] [math]\displaystyle{ x^{33} + x^{24} + x^{20} + x^{18} + x^{12} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ12.1 }[/math]
[math]\displaystyle{ 7.4 }[/math] [math]\displaystyle{ x^{24} + x^{17} + x^{12} + x^{10} + x^6 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ2.1 }[/math]
[math]\displaystyle{ 7.5 }[/math] [math]\displaystyle{ x^{40} + x^{34} + x^{18} + x^{17} + x^5 + x^3 }[/math] [math]\displaystyle{ N^\circ5 }[/math] [math]\displaystyle{ 7:N^\circ1.2 }[/math]
[math]\displaystyle{ 7.6 }[/math] [math]\displaystyle{ x^{48} + x^{40} + x^{18} + x^{10} + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ11.1 }[/math]
[math]\displaystyle{ 7.7 }[/math] [math]\displaystyle{ x^{40} + x^{12} + x^{10} + x^9 + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ2.2 }[/math]
[math]\displaystyle{ 7.8 }[/math] [math]\displaystyle{ x^{34} + x^{24} + x^{10} + x^9 + x^6 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ9.1 }[/math]
[math]\displaystyle{ 7.9 }[/math] [math]\displaystyle{ x^{34} + x^{33} + x^{20} + x^{17} + x^{10} + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ13.1 }[/math]
[math]\displaystyle{ 7.10 }[/math] [math]\displaystyle{ x^{36} + x^{33} + x^{24} + x^9 + x^6 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ10.1 }[/math]
[math]\displaystyle{ 7.11 }[/math] [math]\displaystyle{ x^{40} + x^{36} + x^{20} + x^{10} + x^5 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ10.2 }[/math]
[math]\displaystyle{ 7.12 }[/math] [math]\displaystyle{ x^{36} + x^{34} + x^{20} + x^{10} + x^9 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 7:N^\circ8.1 }[/math]
[math]\displaystyle{ 8 }[/math] [math]\displaystyle{ 8.1 }[/math] [math]\displaystyle{ x^{68} + x^{34} + x^{17} + x^{12} + x^9 + x^3 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ Table 9: N^\circ5.1 }[/math]
[math]\displaystyle{ 8.2 }[/math] [math]\displaystyle{ x^{72} + x^{40} + x^{34} + x^{20} + x^{12} + x^3 }[/math] [math]\displaystyle{ N^\circ5 }[/math] [math]\displaystyle{ 9:N^\circ6.1 }[/math]
[math]\displaystyle{ 8.3 }[/math] [math]\displaystyle{ x^{72} + x^{66} + x^{34} + x^{18} + x^{10} + x^5 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ 9:N^\circ4.1 }[/math]
[math]\displaystyle{ 9 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 10 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]
[math]\displaystyle{ 11 }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math] [math]\displaystyle{ - }[/math]


Table 5: Known classes of quadratic APN polynomials CCZ-inequivalent to APN monomials on [math]\displaystyle{ \mathbb{F}_{2^n} }[/math] [math]\displaystyle{ u }[/math] is primitive in [math]\displaystyle{ \mathbb{F}_{2^n}^* }[/math]}

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