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> | <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> | ||
-</ | <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] |