Geodesic
Improved asymptotic estimates for the numbers of correlation-immune and $k$-resilient vectorial Boolean functions
Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 73-98

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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.
Keywords: random binary mapping, local limit theorem, weights of subfunctions, spectral coefficients, $(n,m,k)$-stable functions, correlation-immune functions. 
@article{DM_2018_30_2_a6,
     author = {K. N. Pankov},
     title = {Improved asymptotic estimates for the numbers of correlation-immune and $k$-resilient vectorial {Boolean} functions},
     journal = {Diskretnaya Matematika},
     pages = {73--98},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_2_a6/}
}
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K. N. Pankov. Improved asymptotic estimates for the numbers of correlation-immune and $k$-resilient vectorial Boolean functions. Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 73-98. http://geodesic.mathdoc.fr/item/DM_2018_30_2_a6/