Geodesic
Perfect colorings of the $12$-cube that attain the bound on correlation immunity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 292-295 
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/
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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 $x=1$.

[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

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