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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Table 1: Classification of Quadratic APN Trinomials (CCZ-inequivalent | Table 1: Classification of Quadratic APN Trinomials (CCZ-inequivalent to infinite monomial | ||
families) in Small Dimensions with Coefficients | families) in Small Dimensions with Coefficients in <math>\mathbb{F}_2</math> | ||
<table> | <table> | ||
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<tr> | <tr> | ||
<td><math>7</math></td> | <td><math>7</math></td> | ||
<td><math>7 | <td><math>7.1</math> | ||
<math>7 | <math>7.2</math> | ||
<td><math>x^{20} + x^6 + x^3</math> | <td><math>x^{20} + x^6 + x^3</math> | ||
<math>x^{ | <math>x^{34} + x^{28} + x^5</math> | ||
<td><math>-</math> | <td><math>-</math> | ||
<math>-</math> | <math>-</math> | ||
Line 34: | Line 34: | ||
<tr> | <tr> | ||
<td><math>8</math></td> | <td><math>8</math></td> | ||
<td><math>8 | <td><math>8.1</math> | ||
<math>8 | <math>8.2</math> | ||
<td><math>x^{72} + x^6 + x^3</math> | <td><math>x^{72} + x^6 + x^3</math> | ||
<math>x^{72} + x^{36} + x^3</math> | <math>x^{72} + x^{36} + x^3</math> | ||
Line 94: | Line 94: | ||
<tr> | <tr> | ||
<td><math>7</math></td> | <td><math>7</math></td> | ||
<td><math>7 | <td><math>7.1</math> | ||
<math>7 | <math>7.2</math> | ||
<math>7 | <math>7.3</math> | ||
<math>7 | <math>7.4</math> | ||
<math>7 | <math>7.5</math> | ||
<math>7 | <math>7.6</math> | ||
<td><math>x^{72} + x^{40} + x^{12} + x^3</math> | <td><math>x^{72} + x^{40} + x^{12} + x^3</math> |
Revision as of 11:08, 18 January 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{ 7.2 }[/math] | [math]\displaystyle{ x^{20} + x^6 + x^3 }[/math]
[math]\displaystyle{ x^{34} + x^{28} + x^5 }[/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] |