Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1

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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]
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