Geodesic
A~bound on correlation immunity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 133-135.

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A new bound on correlation immunity of non-constant unbalanced Boolean functions is proved. The bound is applied to obtain a new necessary condition for existence of a perfect coloring of the hypercube with given parameters. The new bound is stronger than the bounds previously obtained by Bierbrauer and Tarannikov, and is reached on an infinite class of examples. 
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D. G. Fon-Der-Flaass. A~bound on correlation immunity. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 133-135. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a8/

[1] J. Bierbrauer, “Bounds on orthogonal arrays and resilient functions”, Journal of Combinatorial Designs, 3 (1995), 179–183 | DOI | MR | Zbl

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

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

[4] D. Kirienko, “On new infinite family of high order correlation immune unbalanced Boolean functions”, Proceedings of 2002 IEEE International Symposium on Information Theory ISIT'2002 (Lausanne, Switzerland, June 30–July 5, 2002), 465

[5] Tarannikov Yu., Kirienko D., “Spectral analysis of high order correlation immune functions”, Proceedings of 2001 IEEE International Symposium on Information Theory ISIT'2001 (Washington, DC, USA, June 2001), 69

[6] Tarannikov Yu., Korolev P., Botev A., “Autocorrelation coefficients and correlation immunity of Boolean functions”, Advances in cryptology – ASIACRYPT 2001, Proceedings of Asiacrypt 2001 (Gold Coast, Australia, December 9–13, 2001), Lect. Notes in Comp. Sci., 2248, Springer-Verlag, 2001, 460–479 | MR | Zbl

[7] 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