Classification of vectorral Boolean function
This page reports some numerical experiments related to the classification of
vectorial Boolean Functions computed in April 2025.
Definitions
Let m, r, s, t be a positive integers. The space of vectorial Boolean functions
from GF(2)^m into GF(2)^r of degree less or equal to t and valuation greater
or equal s is denoted by V_r(s, t, m). The direct product of the linear
group GL(2, r) by the affine group AG(2, m) acts over the spaces V_r( s, t, m ). Two vectorial
functions f and g in V_r(s, t, m) are said to be s-equivalent when there
exists A in GL(2,r) and B in AG(2, m ) such that
g = A o f o B modulo terms of degree less that s.
One notres that the notion of EA-equivalebce coincides with our notion 2-equivalence...
some class numbers
r=2
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 2 | 3 | 7 | 9 | 18 | 24 | 46 |
s=2 t=2
| 3 | 4 | 5 | 6 | 7 | 8 |
| 2 | 3 | 9 | 132 | 1235402 | 161818045056053 |
s=3 t=3
| 3 | 4 | 5 | 6 | 7 | 8 |
| 5 | 25 | 1352 | 153631102 | 41262807943298102 | 1092387286553048482 |
s=2 t=3
r=3
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 2 | 4 | 13 | 31 | 162 | 1092 | 32389 |
s=2 t=2
s=3 t=3
| 3 | 4 | 5 | 6 |
| 7 | 143 | 21646276 | 187154060013783222 |
s=2 t=3
s=4 t=4
| 3 | 4 | 5 | 6 |
| = | 7 | 1648 | 187154060013783222 |
s=3 t=4
homogeneous quartic maps
| 1 |
2 |
3 | 4 | 5 | 6 |
| 4 |
18 |
162 | 4546 | 204506 | 3299059 |
s=4 t=4 m=6
problem :
find representatives, link with APNs...
(6,3)-bent function
There are 13 ccz classes of (6,3)-bent functions.
problem :
find all APN extension of that bent maps...
[ data ]
Valérie Gillot, Philippe Langevin, Abdoulaye Lo
imath,
last modification : april 2025.