APN Functions
We have used our program for the canonization of linear codes in order to check CCZ-inequivalence of APN-functions f: GF(2n) -> GF(2n) and to calculate their automorphism groups. The codes have length 2n and dimension 2n+1. (w denotes a primitve Element of GF(2n))
These functions were proposed by Carl Bracken, Eimear Byrne, Nadya Markin, Gary McGuire in their paper A few more quadratic APN functions and John Cannon
CCZ-inequivalent APN-functions, n=12:
|
Nr. |
APN-function |
Order of the automorphism group |
Calculation time (in seconds) |
|---|---|---|---|
| 1 | x3 |
201277440 |
360 |
| 4 | w16x768+wx33+x257+w290x544 |
28672 |
??? (modifications by hand necessary) |
| 5 | w16x768+wx33+w290x544 |
114688 |
63000 |
| 6 | w16x768+wx33+x257 |
114688 |
62500 |
| 7 | x993 |
49140 |
97500 |
The codes are all linearly nonisometric since the orders of the automorphism group are all different except for the codes 5 and 6. A closer look on the canonical generator matrix reveals that these codes are also inequivalent.