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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<tr>
<tr>
<td><math>6</math></td>
<td><math>6</math></td>
<td>-</td>
<td><math>-</math></td>
<td>-</td>
<td><math>-</math></td>
<td>-</td>
<td><math>-</math></td>
<td>-</td>
<td><math>-</math></td>
</tr>
</tr>


<tr>
<tr>
<td><math>6</math></td>
<td><math>7</math></td>
<td><math>7,1</math>
<td><math>7,1</math>
<math>7,2</math>
<math>7,2</math>
<td><math>x^{20} + x^6 + x^3</math>
<td><math>x^{20} + x^6 + x^3</math>
<math>x^{65} + x^{10} + x^3</math>
<math>x^{65} + x^{10} + x^3</math>
<td>-
<td><math>-</math>
-</td>
<math>-</math>
<td><math>Table 7: N^\circ8.1</math>
<td><math>Table 7: N^\circ8.1</math>
<math>9:N^\circ1.4</math>
<math>9:N^\circ1.4</math>
</tr>
</tr>
<tr>
<td><math>8</math></td>
<td><math>8,1</math>
<math>8,2</math>
<td><math>x^{72} + x^6 + x^3</math>
<math>x^{72} + x^{36} + x^3</math>
<td><math>-</math>
<math>-</math>
<td><math>Table 7: N^\circ8.1</math>
<math>9:N^\circ1.4</math>
</tr>
<tr>
<td><math>9</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>
<tr>
<td><math>10</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>
<tr>
<td><math>11</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>
</table>
Table 2: Classification of Quadratic APN Quadrinomials (CCZ-inequivalent with infinite monomial
families) in Small Dimensions with Coefficients as 1
<table>
<tr>
<th><math>n</math></th>
<th><math>N^\circ</math></th>
<th>Functions</th>
<th>Families from tables 5</th>
<th>Relation to [6]</th>
</tr>
<tr>
<td><math>6</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>
<tr>
<td><math>7</math></td>
<td><math>7,1</math>
<math>7,2</math>
<math>7,3</math>
<math>7,4</math>
<math>7,5</math>
<math>7,6</math>
<td><math>x^{72} + x^{40} + x^{12} + x^3</math>
<math>x^{33} + x^{17} + x^{12} + x^3</math>
<math>x^{34} + x^{33} + x^{10} + x^3</math>
<math>x^{66} + x^{34} + x^{20} + x^3</math>
<math>x^{68} + x^{18} + x^5 + x^3</math>
<math>x^{66} + x^{18} + x^9 + x^3</math>
<td><math>-</math>
<math>-</math>
<math>-</math>
<math>-</math>
<math>-</math>
<math>-</math>
<td><math>Table 7: N^\circ12.1</math>
<math>7:N^\circ2.2</math>
<math>7:N^\circ10.1</math>
<math>7:N^\circ11.1</math>
<math>7:N^\circ8.1</math>
<math>7:N^\circ9.1</math>
</tr>
<tr>
<td><math>8</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>
<tr>
<td><math>9</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>
<tr>
<td><math>10</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>
<tr>
<td><math>11</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
<td><math>-</math></td>
</tr>
</table>

Revision as of 15:33, 11 January 2019

Table 1: Classification of Quadratic APN Trinomials (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{ 7,2 }[/math]

[math]\displaystyle{ x^{20} + x^6 + x^3 }[/math]

[math]\displaystyle{ x^{65} + x^{10} + x^3 }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ Table 7: N^\circ8.1 }[/math]

[math]\displaystyle{ 9:N^\circ1.4 }[/math]

[math]\displaystyle{ 8 }[/math] [math]\displaystyle{ 8,1 }[/math]

[math]\displaystyle{ 8,2 }[/math]

[math]\displaystyle{ x^{72} + x^6 + x^3 }[/math]

[math]\displaystyle{ x^{72} + x^{36} + x^3 }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ Table 7: N^\circ8.1 }[/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{ 7,2 }[/math]

[math]\displaystyle{ 7,3 }[/math]

[math]\displaystyle{ 7,4 }[/math]

[math]\displaystyle{ 7,5 }[/math]

[math]\displaystyle{ 7,6 }[/math]

[math]\displaystyle{ x^{72} + x^{40} + x^{12} + x^3 }[/math]

[math]\displaystyle{ x^{33} + x^{17} + x^{12} + x^3 }[/math]

[math]\displaystyle{ x^{34} + x^{33} + x^{10} + x^3 }[/math]

[math]\displaystyle{ x^{66} + x^{34} + x^{20} + x^3 }[/math]

[math]\displaystyle{ x^{68} + x^{18} + x^5 + x^3 }[/math]

[math]\displaystyle{ x^{66} + x^{18} + x^9 + x^3 }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ - }[/math]

[math]\displaystyle{ Table 7: N^\circ12.1 }[/math]

[math]\displaystyle{ 7:N^\circ2.2 }[/math]

[math]\displaystyle{ 7:N^\circ10.1 }[/math]

[math]\displaystyle{ 7:N^\circ11.1 }[/math]

[math]\displaystyle{ 7:N^\circ8.1 }[/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]