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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Line 25: | Line 25: | ||
<td><math>x^{20} + x^6 + x^3</math></td> | <td><math>x^{20} + x^6 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 8.1</td> | ||
</tr> | </tr> | ||
Line 32: | Line 32: | ||
<td><math>x^{34} + x^{18} + x^5</math></td> | <td><math>x^{34} + x^{18} + x^5</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 2.1</td> | ||
</tr> | </tr> | ||
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<td><math>x^{72} + x^6 + x^3</math></td> | <td><math>x^{72} + x^6 + x^3</math></td> | ||
<td><math>N^\circ5</math></td> | <td><math>N^\circ5</math></td> | ||
<td | <td>Table 9: № 1.3</td> | ||
</tr> | </tr> | ||
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<td><math>x^{72} + x^{36} + x^3</math></td> | <td><math>x^{72} + x^{36} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 9: № 1.4</td> | ||
</tr> | </tr> | ||
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<td><math>x^{72} + x^{40} + x^{12} + x^3</math></td> | <td><math>x^{72} + x^{40} + x^{12} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 12.1</td> | ||
</tr> | </tr> | ||
Line 107: | Line 107: | ||
<td><math>x^{33} + x^{17} + x^{12} + x^3</math></td> | <td><math>x^{33} + x^{17} + x^{12} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 2.2</td> | ||
</tr> | </tr> | ||
Line 113: | Line 113: | ||
<td><math>x^{34} + x^{33} + x^{10} + x^3</math></td> | <td><math>x^{34} + x^{33} + x^{10} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 10.1</td> | ||
</tr> | </tr> | ||
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<td><math>x^{66} + x^{34} + x^{20} + x^3</math></td> | <td><math>x^{66} + x^{34} + x^{20} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 11.1</td> | ||
</tr> | </tr> | ||
Line 125: | Line 125: | ||
<td><math>x^{68} + x^{18} + x^5 + x^3</math></td> | <td><math>x^{68} + x^{18} + x^5 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 8.1</td> | ||
</tr> | </tr> | ||
Line 131: | Line 131: | ||
<td><math>x^{66} + x^{18} + x^9 + x^3</math></td> | <td><math>x^{66} + x^{18} + x^9 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 9.1</td> | ||
</tr> | </tr> | ||
Line 193: | Line 193: | ||
<td><math>x^{68} + x^{40} + x^{24} + x^6 + x^3</math></td> | <td><math>x^{68} + x^{40} + x^{24} + x^6 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 13.1</td> | ||
</tr> | </tr> | ||
Line 199: | Line 199: | ||
<td><math>x^{65} + x^{20} + x^{18} + x^6 + x^3</math></td> | <td><math>x^{65} + x^{20} + x^{18} + x^6 + x^3</math></td> | ||
<td><math>N^\circ5</math></td> | <td><math>N^\circ5</math></td> | ||
<td | <td>Table 7: № 1.2</td> | ||
</tr> | </tr> | ||
Line 205: | Line 205: | ||
<td><math>x^{40} + x^{34} + x^{18} + x^{10} + x^3</math></td> | <td><math>x^{40} + x^{34} + x^{18} + x^{10} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 12.1</td> | ||
</tr> | </tr> | ||
Line 211: | Line 211: | ||
<td><math>x^{48} + x^{40} + x^{10} + x^9 + x^3</math></td> | <td><math>x^{48} + x^{40} + x^{10} + x^9 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 1.2</td> | ||
</tr> | </tr> | ||
Line 217: | Line 217: | ||
<td><math>x^{33} + x^9 + x^6 + x^5 + x^3</math></td> | <td><math>x^{33} + x^9 + x^6 + x^5 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 11.1</td> | ||
</tr> | </tr> | ||
Line 223: | Line 223: | ||
<td><math>x^{40} + x^{36} + x^{34} + x^{24} + x^3</math></td> | <td><math>x^{40} + x^{36} + x^{34} + x^{24} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 10.1</td> | ||
</tr> | </tr> | ||
Line 229: | Line 229: | ||
<td><math>x^{24} + x^{10} + x^9 + x^6 + x^3</math></td> | <td><math>x^{24} + x^{10} + x^9 + x^6 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 2.1</td> | ||
</tr> | </tr> | ||
Line 235: | Line 235: | ||
<td><math>x^{65} + x^{36} + x^{20} + x^{17} + x^3</math></td> | <td><math>x^{65} + x^{36} + x^{20} + x^{17} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 14.1</td> | ||
</tr> | </tr> | ||
Line 241: | Line 241: | ||
<td><math>x^{40} + x^{33} + x^{17} + x^5 + x^3</math></td> | <td><math>x^{40} + x^{33} + x^{17} + x^5 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 8.1</td> | ||
</tr> | </tr> | ||
Line 247: | Line 247: | ||
<td><math>x^{36} + x^{33} + x^{18} + x^9 + x^5</math></td> | <td><math>x^{36} + x^{33} + x^{18} + x^9 + x^5</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 10.1</td> | ||
</tr> | </tr> | ||
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<td><math>x^{36} + x^{33} + x^9 + x^6 + x^3</math></td> | <td><math>x^{36} + x^{33} + x^9 + x^6 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 9: № 1.4</td> | ||
</tr> | </tr> | ||
Line 261: | Line 261: | ||
<td><math>x^{72} + x^{66} + x^{12} + x^6 + x^3</math></td> | <td><math>x^{72} + x^{66} + x^{12} + x^6 + x^3</math></td> | ||
<td><math>N^\circ5</math></td> | <td><math>N^\circ5</math></td> | ||
<td | <td>Table 9: № 1.3</td> | ||
</tr> | </tr> | ||
Line 267: | Line 267: | ||
<td><math>x^{130} + x^{66} + x^{40} + x^{12} + x^3</math></td> | <td><math>x^{130} + x^{66} + x^{40} + x^{12} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 9: № 6.1</td> | ||
</tr> | </tr> | ||
Line 273: | Line 273: | ||
<td><math>x^{66} + x^{40} + x^{18} + x^5 + x^3</math></td> | <td><math>x^{66} + x^{40} + x^{18} + x^5 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 9: № 5.1</td> | ||
</tr> | </tr> | ||
Line 351: | Line 351: | ||
<td><math>x^{34} + x^{33} + x^{12} + x^6 + x^5 + x^3</math></td> | <td><math>x^{34} + x^{33} + x^{12} + x^6 + x^5 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 14.2</td> | ||
</tr> | </tr> | ||
Line 357: | Line 357: | ||
<td><math>x^{40} + x^{24} + x^{20} + x^9 + x^5 + x^3</math></td> | <td><math>x^{40} + x^{24} + x^{20} + x^9 + x^5 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 14.1</td> | ||
</tr> | </tr> | ||
Line 363: | Line 363: | ||
<td><math>x^{33} + x^{24} + x^{20} + x^{18} + x^{12} + x^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>-</math></td> | ||
<td | <td>Table 7: № 12.1</td> | ||
</tr> | </tr> | ||
Line 369: | Line 369: | ||
<td><math>x^{24} + x^{17} + x^{12} + x^{10} + x^6 + x^3</math></td> | <td><math>x^{24} + x^{17} + x^{12} + x^{10} + x^6 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 2.1</td> | ||
</tr> | </tr> | ||
Line 375: | Line 375: | ||
<td><math>x^{40} + x^{34} + x^{18} + x^{17} + x^5 + x^3</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>N^\circ5</math></td> | ||
<td | <td>Table 7: № 1.2</td> | ||
</tr> | </tr> | ||
Line 381: | Line 381: | ||
<td><math>x^{48} + x^{40} + x^{18} + x^{10} + x^5 + x^3</math></td> | <td><math>x^{48} + x^{40} + x^{18} + x^{10} + x^5 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 11.1</td> | ||
</tr> | </tr> | ||
Line 387: | Line 387: | ||
<td><math>x^{40} + x^{12} + x^{10} + x^9 + x^5 + x^3</math></td> | <td><math>x^{40} + x^{12} + x^{10} + x^9 + x^5 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 2.2</td> | ||
</tr> | </tr> | ||
Line 393: | Line 393: | ||
<td><math>x^{34} + x^{24} + x^{10} + x^9 + x^6 + x^3</math></td> | <td><math>x^{34} + x^{24} + x^{10} + x^9 + x^6 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 9.1</td> | ||
</tr> | </tr> | ||
Line 399: | Line 399: | ||
<td><math>x^{34} + x^{33} + x^{20} + x^{17} + x^{10} + x^3</math></td> | <td><math>x^{34} + x^{33} + x^{20} + x^{17} + x^{10} + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 13.1</td> | ||
</tr> | </tr> | ||
Line 405: | Line 405: | ||
<td><math>x^{36} + x^{33} + x^{24} + x^9 + x^6 + x^3</math> | <td><math>x^{36} + x^{33} + x^{24} + x^9 + x^6 + x^3</math> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 10.1</td> | ||
</tr> | </tr> | ||
Line 411: | Line 411: | ||
<td><math>x^{40} + x^{36} + x^{20} + x^{10} + x^5 + x^3</math></td> | <td><math>x^{40} + x^{36} + x^{20} + x^{10} + x^5 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 10.2</td> | ||
</tr> | </tr> | ||
Line 417: | Line 417: | ||
<td><math>x^{36} + x^{34} + x^{20} + x^{10} + x^9 + x^3</math></td> | <td><math>x^{36} + x^{34} + x^{20} + x^{10} + x^9 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 7: № 8.1</td> | ||
</tr> | </tr> | ||
Line 425: | Line 425: | ||
<td><math>x^{68} + x^{34} + x^{17} + x^{12} + x^9 + x^3</math></td> | <td><math>x^{68} + x^{34} + x^{17} + x^{12} + x^9 + x^3</math></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 9: № 5.1</td> | ||
</tr> | </tr> | ||
Line 431: | Line 431: | ||
<td><math>x^{72} + x^{40} + x^{34} + x^{20} + x^{12} + x^3</math></td> | <td><math>x^{72} + x^{40} + x^{34} + x^{20} + x^{12} + x^3</math></td> | ||
<td><math>N^\circ5</math></td> | <td><math>N^\circ5</math></td> | ||
<td | <td>Table 9: № 6.1</td> | ||
</tr> | </tr> | ||
Line 437: | Line 437: | ||
<td><math>x^{72} + x^{66} + x^{34} + x^{18} + x^{10} + x^5</math></td></td> | <td><math>x^{72} + x^{66} + x^{34} + x^{18} + x^{10} + x^5</math></td></td> | ||
<td><math>-</math></td> | <td><math>-</math></td> | ||
<td | <td>Table 9: № 4.1</td> | ||
</tr> | </tr> | ||
Revision as of 13:59, 27 February 2019
The following tables list CCZ-inequivalent representatives found by systematically searching for APN functions among all trinomials, quadrinomials, pentanomials and hexanomials with coefficients in [math]\displaystyle{ \mathbb{F}_{2} }[/math] over [math]\displaystyle{ \mathbb{F}_{2^n} }[/math] with [math]\displaystyle{ 6 \le n \le 11 }[/math] [1]. The tables also list which equivalence class from [2] the functions belong to. Only polynomials inequivalent to power functions are considered. If the polynomial is equivalent to a family from the table of infinite families, this is also listed.
Trinomials
[math]\displaystyle{ n }[/math] | [math]\displaystyle{ N^\circ }[/math] | Functions | Familiy | Relation to [2] |
---|---|---|---|---|
[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] | Table 7: № 8.1 |
[math]\displaystyle{ 7.2 }[/math] | [math]\displaystyle{ x^{34} + x^{18} + x^5 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 2.1 | |
[math]\displaystyle{ 8 }[/math] | [math]\displaystyle{ 8.1 }[/math] | [math]\displaystyle{ x^{72} + x^6 + x^3 }[/math] | [math]\displaystyle{ N^\circ5 }[/math] | Table 9: № 1.3 |
[math]\displaystyle{ 8.2 }[/math] | [math]\displaystyle{ x^{72} + x^{36} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 9: № 1.4 | |
[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] |
Quadrinomials
[math]\displaystyle{ n }[/math] | [math]\displaystyle{ N^\circ }[/math] | Functions | Families | Relation to [2] |
---|---|---|---|---|
[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] | Table 7: № 12.1 |
[math]\displaystyle{ 7.2 }[/math] | [math]\displaystyle{ x^{33} + x^{17} + x^{12} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 2.2 | |
[math]\displaystyle{ 7.3 }[/math] | [math]\displaystyle{ x^{34} + x^{33} + x^{10} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 10.1 | |
[math]\displaystyle{ 7.4 }[/math] | [math]\displaystyle{ x^{66} + x^{34} + x^{20} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 11.1 | |
[math]\displaystyle{ 7.5 }[/math] | [math]\displaystyle{ x^{68} + x^{18} + x^5 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 8.1 | |
[math]\displaystyle{ 7.6 }[/math] | [math]\displaystyle{ x^{66} + x^{18} + x^9 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 9.1 | |
[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] |
Pentanomials
[math]\displaystyle{ n }[/math] | [math]\displaystyle{ N^\circ }[/math] | Functions | Families | Relation to [2] |
---|---|---|---|---|
[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] | Table 7: № 13.1 |
[math]\displaystyle{ 7.2 }[/math] | [math]\displaystyle{ x^{65} + x^{20} + x^{18} + x^6 + x^3 }[/math] | [math]\displaystyle{ N^\circ5 }[/math] | Table 7: № 1.2 | |
[math]\displaystyle{ 7.3 }[/math] | [math]\displaystyle{ x^{40} + x^{34} + x^{18} + x^{10} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 12.1 | |
[math]\displaystyle{ 7.4 }[/math] | [math]\displaystyle{ x^{48} + x^{40} + x^{10} + x^9 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 1.2 | |
[math]\displaystyle{ 7.5 }[/math] | [math]\displaystyle{ x^{33} + x^9 + x^6 + x^5 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 11.1 | |
[math]\displaystyle{ 7.6 }[/math] | [math]\displaystyle{ x^{40} + x^{36} + x^{34} + x^{24} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 10.1 | |
[math]\displaystyle{ 7.7 }[/math] | [math]\displaystyle{ x^{24} + x^{10} + x^9 + x^6 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 2.1 | |
[math]\displaystyle{ 7.8 }[/math] | [math]\displaystyle{ x^{65} + x^{36} + x^{20} + x^{17} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 14.1 | |
[math]\displaystyle{ 7.9 }[/math] | [math]\displaystyle{ x^{40} + x^{33} + x^{17} + x^5 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 8.1 | |
[math]\displaystyle{ 7.10 }[/math] | [math]\displaystyle{ x^{36} + x^{33} + x^{18} + x^9 + x^5 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 10.1 | |
[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] | Table 9: № 1.4 |
[math]\displaystyle{ 8.2 }[/math] | [math]\displaystyle{ x^{72} + x^{66} + x^{12} + x^6 + x^3 }[/math] | [math]\displaystyle{ N^\circ5 }[/math] | Table 9: № 1.3 | |
[math]\displaystyle{ 8.3 }[/math] | [math]\displaystyle{ x^{130} + x^{66} + x^{40} + x^{12} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 9: № 6.1 | |
[math]\displaystyle{ 8.4 }[/math] | [math]\displaystyle{ x^{66} + x^{40} + x^{18} + x^5 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 9: № 5.1 | |
[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] |
Hexanomials
[math]\displaystyle{ n }[/math] | [math]\displaystyle{ N^\circ }[/math] | Functions | Families | Relation to [2] |
---|---|---|---|---|
[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] | Table 7: № 14.2 |
[math]\displaystyle{ 7.2 }[/math] | [math]\displaystyle{ x^{40} + x^{24} + x^{20} + x^9 + x^5 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 14.1 | |
[math]\displaystyle{ 7.3 }[/math] | [math]\displaystyle{ x^{33} + x^{24} + x^{20} + x^{18} + x^{12} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 12.1 | |
[math]\displaystyle{ 7.4 }[/math] | [math]\displaystyle{ x^{24} + x^{17} + x^{12} + x^{10} + x^6 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 2.1 | |
[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] | Table 7: № 1.2 | |
[math]\displaystyle{ 7.6 }[/math] | [math]\displaystyle{ x^{48} + x^{40} + x^{18} + x^{10} + x^5 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 11.1 | |
[math]\displaystyle{ 7.7 }[/math] | [math]\displaystyle{ x^{40} + x^{12} + x^{10} + x^9 + x^5 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 2.2 | |
[math]\displaystyle{ 7.8 }[/math] | [math]\displaystyle{ x^{34} + x^{24} + x^{10} + x^9 + x^6 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 9.1 | |
[math]\displaystyle{ 7.9 }[/math] | [math]\displaystyle{ x^{34} + x^{33} + x^{20} + x^{17} + x^{10} + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 13.1 | |
[math]\displaystyle{ 7.10 }[/math] | [math]\displaystyle{ x^{36} + x^{33} + x^{24} + x^9 + x^6 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 10.1 | |
[math]\displaystyle{ 7.11 }[/math] | [math]\displaystyle{ x^{40} + x^{36} + x^{20} + x^{10} + x^5 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 10.2 | |
[math]\displaystyle{ 7.12 }[/math] | [math]\displaystyle{ x^{36} + x^{34} + x^{20} + x^{10} + x^9 + x^3 }[/math] | [math]\displaystyle{ - }[/math] | Table 7: № 8.1 | |
[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] | Table 9: № 5.1 |
[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] | Table 9: № 6.1 | |
[math]\displaystyle{ 8.3 }[/math] | [math]\displaystyle{ x^{72} + x^{66} + x^{34} + x^{18} + x^{10} + x^5 }[/math] | [math]\displaystyle{ - }[/math] | Table 9: № 4.1 | |
[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] |