Geodesic
On almost balanced Boolean functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 23-25.

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A Boolean function is called correlation-immune of degree $n-m$ if it takes the value $1$ the same number of times for each $m$-dimensional face of the hypercube. Balanced correlation-immune function is called resilient. The almost balanced (or almost resilient) Boolean function is defined as a function taking values $1$ in a half or in a half plus or minus one of vertices in each face. Here, some constructions of almost balanced functions are proposed, some properties and a low bound for the number of these functions are established. 
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V. N. Potapov. On almost balanced Boolean functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 23-25. http://geodesic.mathdoc.fr/item/PDMA_2012_5_a11/

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