APN functions obtained via polynomial expansion in small dimensions
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| ID | Representative | Equivalent to | Orthoderivative diff. spec. |
|---|---|---|---|
| 8.1 | [math]\displaystyle{ \alpha^{170}x^{192} + \alpha^{85}x^{132} + x^6 + x^3 }[/math] | SW 19 | [math]\displaystyle{ 0^{37872}, 2^{22788}, 4^{4068}, 6^{492}, 8^{60} }[/math] |
| 8.2 | [math]\displaystyle{ x^{66} + \alpha^{85}x^{33} + x^{18} + x^9 + x^3 }[/math] | SW 11 | [math]\displaystyle{ 0^{38040}, 2^{22461}, 4^{4218}, 6^{513}, 8^{36}, 10^{12} }[/math] |
| 8.3 | [math]\displaystyle{ x^{66} + \alpha^{85}x^{33} + \alpha^{17}x^9 + \alpha^{102}x^6 + x^3 }[/math] | SW 13 | [math]\displaystyle{ 0^{38076}, 2^{22311}, 4^{4374}, 6^{495}, 8^{24} }[/math] |
| 8.4 | [math]\displaystyle{ \alpha^{85}x^{132} + \alpha^{85}x^{72} + x^9 + x^6 + x^3 }[/math] | SW 12 | [math]\displaystyle{ 0^{38160}, 2^{22104}, 4^{4536}, 6^{456}, 8^{24} }[/math] |
| 8.5 | [math]\displaystyle{ x^{66} + x^{12} + \alpha^{85}x^6 + x^3 }[/math] | SW 6 | [math]\displaystyle{ 0^{38160}, 2^{22164}, 4^{4428}, 6^{492}, 8^{36} }[/math] |
| 8.6 | [math]\displaystyle{ x^{129} + \alpha^{85}x^{24} + x^{12} + x^9 + x^3 }[/math] | SW 8 | [math]\displaystyle{ 0^{38184}, 2^{22179}, 4^{4338}, 6^{531}, 8^{48} }[/math] |
| 8.7 | [math]\displaystyle{ \alpha^{170}x^{132} + \alpha^{85}x^{66} + \alpha^{85}x^{18} + x^3 }[/math] | new | [math]\displaystyle{ 0^{38196}, 2^{22008}, 4^{4608}, 6^{456}, 8^{12} }[/math] |
| 8.8 | [math]\displaystyle{ \alpha^{85}x^{132} + \alpha^{85}x^{72} + x^{36} + x^{24} + x^3 }[/math] | SW 9 | [math]\displaystyle{ 0^{38256}, 2^{22116}, 4^{4230}, 6^{648}, 8^{30} }[/math] |
| 8.9 | [math]\displaystyle{ \alpha^{85}x^{192} + x^{72} + x^{33} + x^{24} + x^9 + \alpha^{153}x^6 }[/math] | SW 17 | [math]\displaystyle{ 0^{38388}, 2^{21723}, 4^{4626}, 6^{507}, 8^{36} }[/math] |
| 8.10 | [math]\displaystyle{ \alpha^{221}x^{96} + \alpha^{221}x^{33} + x^{12} + x^9 + x^6 + \alpha^{187}*x^3 }[/math] | SW 10 | [math]\displaystyle{ 0^{38439}, 2^{21618}, 4^{4671}, 6^{528}, 8^{24} }[/math] |
| 8.11 | [math]\displaystyle{ \alpha^{238}x^{144} + x^{132} + \alpha^{51}x^{96} + \alpha^{119}x^{48} + x^{33} + x^9 }[/math] | SW 16 | [math]\displaystyle{ 0^{38457}, 2^{21552}, 4^{4743}, 6^{510}, 8^{18} }[/math] |
| 8.12 | [math]\displaystyle{ \alpha^{204}x^{160} + \alpha^{51}x^{48} + \alpha^{102}x^{12} + \alpha^{204}x^{10} + x^9 }[/math] | SW 22 | [math]\displaystyle{ 0^{38844}, 2^{20974}, 4^{4764}, 6^{654}, 8^{44} }[/math] |
| 8.13 | [math]\displaystyle{ \alpha^{160}x^{132} + \alpha^{10}x^{72} + x^{48} + \alpha x^{34} + \alpha^3x^{33} + \alpha^{48}x^{18} + x^{17} + x^3 }[/math] | B 31 | [math]\displaystyle{ 0^{39150}, 2^{20463}, 4^{4920}, 6^{675}, 8^{54}, 10^{12}, 12^6 }[/math] |
| 8.14 | [math]\displaystyle{ x^{144} + \alpha^{85}x^{96} + \alpha^{170}x^{80} + \alpha^{85}x^{65} + \alpha^{85}x^{17} + x^9 + x^5 }[/math] | B 12668 | [math]\displaystyle{ 0^{39408}, 2^{20072}, 4^{4922}, 6^{798}, 8^{70}, 10^{10} }[/math] |
| 8.15 | [math]\displaystyle{ x^{66} + \alpha^{170}x^{40} + x^{18} + \alpha^{85}x^5 + x^3 }[/math] | Y 4346 | [math]\displaystyle{ 0^{39408}, 2^{20218}, 4^{4692}, 6^{838}, 8^{104}, 10^{12}, 12^8 }[/math] |
| 8.16 | [math]\displaystyle{ x^{160} + x^{132} + x^{80} + x^{68} + x^6 + x^3 }[/math] | SW 20 | [math]\displaystyle{ 0^{39692}, 2^{19752}, 4^{4756}, 6^{978}, 8^{72}, 10^{26}, 12^4 }[/math] |