Geodesic
Perfect colorings of the $12$-cube that attain the bound on correlation immunity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 292-295.

Voir la notice de l'article provenant de la source Math-Net.Ru

We construct perfect $2$-colorings of the $12$-hypercube that attain our recent bound on the dimension of arbitrary correlation immune functions. We prove that such colorings with parameters $(x,12-x,4+x,8-x)$ exist if $x=0,2,3$ and do not exist if $x=1$. 
@article{SEMR_2007_4_a17,
     author = {D. G. Fon-Der-Flaass},
     title = {Perfect colorings of the $12$-cube that attain the bound on correlation immunity},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {292--295},
     publisher = {mathdoc},
     volume = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a17/}
}
TY  - JOUR
AU  - D. G. Fon-Der-Flaass
TI  - Perfect colorings of the $12$-cube that attain the bound on correlation immunity
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2007
SP  - 292
EP  - 295
VL  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2007_4_a17/
LA  - ru
ID  - SEMR_2007_4_a17
ER  - 
%0 Journal Article
%A D. G. Fon-Der-Flaass
%T Perfect colorings of the $12$-cube that attain the bound on correlation immunity
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2007
%P 292-295
%V 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2007_4_a17/
%G ru
%F SEMR_2007_4_a17
D. G. Fon-Der-Flaass. Perfect colorings of the $12$-cube that attain the bound on correlation immunity. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 292-295. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a17/

[1] D. Fon-Der-Flaass, “Perfect colorings of a hypercube”, Siberian Math. J. (to appear)

[2] D. G. Fon-Der-Flaass, “A bound on correlation immunity”, Siberian Electronic Mathematical Reports, 4 (2007), 133–135 | MR | Zbl

[3] C. Godsil, “Equitable partitions”, Combinatorics, Paul Erdős is Eighty, v. 1, Keszthely (Hungary), 1993, 173–192 | MR | Zbl

[4] Tarannikov Yu., On resilient Boolean functions with maximal possible nonlinearity, Report 2000/005, March 2000, 18 pp. ; Cryptology ePrint archive http://eprint.iacr.org | MR