# Difference between revisions of "CCZ-inequivalent representatives from the known APN families for dimensions up to 11"

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CCZ-inequivalent APN Functions over <math>\mathbb{F}_{2^n}</math> from the Known APN Classes for <math>6\leqslant n \leqslant 11</math> | CCZ-inequivalent APN Functions over <math>\mathbb{F}_{2^n}</math> from the Known APN Classes for <math>6\leqslant n \leqslant 11</math> | ||

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+ | The function families are indexed according to the table of [[Known infinite families of APN power functions over GF(2^n)]] in the case of monomials, and according to the table of [[Known infinite families of quadratic APN polynomials over GF(2^n)]] in the case of polynomial families. | ||

<table class="borderless"> | <table class="borderless"> |

## Revision as of 15:14, 11 September 2019

CCZ-inequivalent APN Functions over from the Known APN Classes for

The function families are indexed according to the table of Known infinite families of APN power functions over GF(2^n) in the case of monomials, and according to the table of Known infinite families of quadratic APN polynomials over GF(2^n) in the case of polynomial families.

Dimension | N^{○} |
Functions | Equivalent to | Walsh spectrum | Γ-rank | Δ-rank |
---|---|---|---|---|---|---|

6 | 6.1 | x^{3} |
Gold | Gold | 1102 | 94 |

6.2 | x^{24}+ax^{17}+a^{8}x^{10}+ax^{9}+x^{3} |
C3 | Gold | 1146 | 94 | |

6.3 | ax^{3}+x^{17}+a^{4}x^{24} |
C7-C9 | Gold | 1166 | 96 | |

7 | 7.1 | x^{3} |
Gold | Gold | 3610 | 198 |

7.2 | x^{5} |
Gold | Gold | 3708 | 198 | |

7.3 | x^{9} |
Gold | Gold | 3610 | 198 | |

7.4 | x^{13} |
Kasami | Gold | 4270 | 338 | |

7.5 | x^{57} |
Kasami | Gold | 4704 | 436 | |

7.6 | x^{63} |
Inverse | Inverse | 8128 | 4928 | |

7.7 | x^{3}+Tr_{7}(x^{9}) |
C4 | Gold | 4026 | 212 | |

8 | 8.1 | x^{3} |
Gold | Gold | 11818 | 420 |

8.2 | x^{9} |
Gold | Gold | 12370 | 420 | |

8.3 | x^{57} |
Kasami | Gold | 15358 | 960 | |

8.4 | x^{3}+x^{17}+p^{48}x^{18}+p^{3}x^{33}+px^{34}+x^{48} |
C3 | Gold | 13200 | 414 | |

8.5 | x^{3}+Tr_{8}(x^{9}) |
C4 | Gold | 13200 | 432 | |

8.6 | x^{3}+a^{-1}Tr_{8}(a^{3}x^{9}) |
C4 | Gold | 13842 | 436 | |

8.7 | a(x+x^{16})(ax+a^{16}x^{16})+a^{17}(ax+a^{16}x^{16})^{12} |
C10 | Gold | 13642 | 436 | |

9 | 9.1 | x^{3} |
Gold | Gold | 38470 | 872 |

9.2 | x^{5} |
Gold | Gold | 41494 | 872 | |

9.3 | x^{17} |
Gold | Gold | 38470 | 872 | |

9.4 | x^{13} |
Kasami | Gold | 58676 | 3086 | |

9.5 | x^{241} |
Kasami | Gold | 61726 | 3482 | |

9.6 | x^{19} |
Welch | Gold | 60894 | 3956 | |

9.7 | x^{255} |
Inverse | Inverse | 130816 | 93024 | |

9.8 | x^{3}+Tr_{9}(x^{9}) |
C4 | Gold | 47890 | 920 | |

9.9 | x^{3}+Tr^{3}_{9}(x^{9}+x^{18}) |
C5 | Gold | 48428 | 930 | |

9.10 | x^{3}+Tr^{3}_{9}(x^{18}+x^{36}) |
C6 | Gold | 48460 | 944 | |

9.11 | x^{3}+a^{246}x^{10}+a^{47}x^{17}+a^{181}x^{66}+a^{428}x^{129} |
C11 | Gold | 48596 | 944 | |

10 | 10.1 | x^{3} |
Gold | Gold | 125042 | |

10.2 | x^{9} |
Gold | Gold | 136492 | ||

10.3 | x^{57} |
Kasami | Gold | 186416 | ||

10.4 | x^{339} |
Dobbertin | Dobbertin | 280604 | ||

10.5 | x^{6}+x^{33}+p^{31}x^{192} |
C3 | Gold | 151216 | ||

10.6 | x^{33}+x^{72}+p^{31}x^{258} |
C3 | Gold | 153896 | ||

10.7 | x^{3}+Tr_{10}(x^{9}) |
C4 | Gold | 164034 | ||

10.8 | x^{3}+a^{-1}Tr_{10}(a^{3}x^{9}) |
C4 | Gold | 164098 | ||

10.9 | x^{3} + p^{341}x^{9} + p^{682}x^{96} + x^{288} |
C12 | Gold | 166068 | ||

10.10 | x^{3} + p^{341}x^{129} + p^{682}x^{96} + x^{36} |
C12 | Gold | 166168 | ||

11 | 11.1 | x^{3} |
Gold | Gold | ||

11.2 | x^{5} |
Gold | Gold | |||

11.3 | x^{9} |
Gold | Gold | |||

11.4 | x^{17} |
Gold | Gold | |||

11.5 | x^{33} |
Gold | Gold | |||

11.6 | x^{13} |
Kasami | Gold | |||

11.7 | x^{57} |
Kasami | Gold | |||

11.8 | x^{241} |
Kasami | Gold | |||

11.9 | x^{993} |
Kasami | Gold | |||

11.10 | x^{35} |
Welch | Gold | |||

11.11 | x^{287} |
Niho | Gold | |||

11.12 | x^{1023} |
Inverse | Inverse | |||

11.13 | x^{3}+Tr_{11}(x^{9}) |
C4 | Gold |