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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The following tables list CCZ-inequivalent representatives found by systematically searching for APN functions among all trinomials, quadrinomials, pentanomials and hexanomials with coefficients in over with [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

Dimension Functions Familiy Relation to [2]
Table 7: № 8.1
Table 7: № 2.1
Table 9: № 1.3
Table 9: № 1.4

Quadrinomials

Dimension Functions Families Relation to [2]
Table 7: № 12.1
Table 7: № 2.2
Table 7: № 10.1
Table 7: № 11.1
Table 7: № 8.1
Table 7: № 9.1

Pentanomials

Dimension Functions Families Relation to [2]
Table 7: № 13.1
Table 7: № 1.2
Table 7: № 12.1
Table 7: № 1.2
Table 7: № 11.1
Table 7: № 10.1
Table 7: № 2.1
Table 7: № 14.1
Table 7: № 8.1
Table 7: № 10.1
Table 9: № 1.4
Table 9: № 1.3
Table 9: № 6.1
Table 9: № 5.1

Hexanomials

Dimension Functions Families Relation to [2]
Table 7: № 14.2
Table 7: № 14.1
Table 7: № 12.1
Table 7: № 2.1
Table 7: № 1.2
Table 7: № 11.1
Table 7: № 2.2
Table 7: № 9.1
Table 7: № 13.1
Table 7: № 10.1
Table 7: № 10.2
Table 7: № 8.1
Table 9: № 5.1
Table 9: № 6.1
Table 9: № 4.1
  1. Sun B. On Classification and Some Properties of APN Functions.
  2. 2.0 2.1 2.2 2.3 2.4 Edel Y, Pott A. A new almost perfect nonlinear function which is not quadratic. Adv. in Math. of Comm.. 2009 Mar;3(1):59-81.