Sigma multiplicities for APN functions in dimensions up to 10

From Boolean
Revision as of 15:29, 2 December 2020 by Nikolay (talk | contribs) (Created page with "For all known APN functions over GF(2^n) with n up to 10, the following tables list the partitions of GF(2^n) induced by the multiplicities of the Sigma sets <math>\Sigma_F^k(...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

For all known APN functions over GF(2^n) with n up to 10, the following tables list the partitions of GF(2^n) induced by the multiplicities of the Sigma sets <math>\Sigma_F^k(0)</sigma> for k = 4, as explained in the SETA paper on testing EA-equivalences.

Due to the large number of functions, the results for dimension 8 are listed on a separate page.

Dimension 9

Dimension 10

Functions 1-10 are indexed according to [[1]]. The remaining functions correspond to the ones found via self-equivalences, and are indexed in the same way as in the provided dataset.

IDPartition sizes
1 1, 341, 682
2 1, 341, 682
3 1, 341, 682
4 1, 341, 682
5 1, 341, 682
6 1, 341, 682
7 1, 341, 682
8 1, 341, 682
9 1, 341, 682
10 1, 341, 682
11 1, 31, 155, 155, 155, 217, 310
12 1, 341, 682
13 1, 124, 217, 310, 372
14 1, 341, 682
15 1, 11, 11, 165, 330, 506