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Perfect colorings of the 12-cube that attain the bound on correlation immunity. (Russian. English summary) Zbl 1132.05314
Summary: 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 $$x = 1$$.

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
Boolean function; maximal nonlinearity
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