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A bound on correlation immunity. (English) Zbl 1132.05309
Summary: 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 J. Bierbrauer [J. Comb. Des. 3, No. 3, 179–183 (1995; Zbl 0886.05034)] and Yu. Tarannikov [Cryptology ePrint Archive, Report 2000/069], and is reached on an infinite class of examples.

MSC:
05B15 Orthogonal arrays, Latin squares, Room squares
68P25 Data encryption (aspects in computer science)
94A60 Cryptography
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