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We refine local limit theorems for the distribution of a part of the weight vector of subfunctions and for the distribution of a part of the vector of spectral coefficients of linear combinations of coordinate functions of a random binary mapping. These theorems are used to derive improved asymptotic estimates for the numbers of correlation-immune and  k -resilient vectorial Boolean functions.

Improved asymptotic estimates for the numbers of correlation-immune and k -resilient vectorial Boolean functions