Geodesic
A local limit theorem for the distribution of a part of the spectrum of a random binary function
Diskretnaya Matematika, Tome 12 (2000) no. 1, pp. 82-95

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We obtain a local limit theorem for the distribution of the vector (of growing dimension) consisting of some spectral coefficients of a random binary function of $n$ variables as $n\to\infty$. We correct a mistake in the asymptotic formula for the number of correlation-immune functions of order $k$ obtained in previous author's paper. We prove an asymptotic formula for the number of $(n,1,k)$-resilient functions as $n\to\infty$ and $k=k(n)=o(\sqrt n)$. 
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     author = {O. V. Denisov},
     title = {A local limit theorem for the distribution of a part of the spectrum of a random binary function},
     journal = {Diskretnaya Matematika},
     pages = {82--95},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2000_12_1_a6/}
}
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O. V. Denisov. A local limit theorem for the distribution of a part of the spectrum of a random binary function. Diskretnaya Matematika, Tome 12 (2000) no. 1, pp. 82-95. http://geodesic.mathdoc.fr/item/DM_2000_12_1_a6/