A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity

Abstract

АннотацияThe number of n-ary balanced correlation immune (resilient) Boolean functions of order n 2 is not less than n 2 (n/2)−2 (1+o(1)) as n → ∞.

On the number of frequency hypercubes $F^n(4;2,2)$

“…As follows from the definition, double-MDS-codes are equivalent to simple orthogonal arrays OA(2 2n−1 , n, 4, n − 1), see [3] for the definition and notation. In [11], based on a lower bound on the number of double-MDS-codes, Potapov derived a lower bound on the number of n-ary balanced correlation immune (resilient) Boolean functions of order n/2 (equivalently, simple orthogonal arrays OA(2 n−1 , n, 2, n/2)). Substituting the results of our computing of the number of F 4 (4; 2, 2) to his arguments straightforwardly improves this lower bound for n = 8.…”