Abstract
We provide an upper bound on binomial coefficients that holds over the entire parameter range an whose form repeats the form of the de Moivre – Laplace approximation of the symmetric binomial distribution. Using the bound, we estimate the number of continuations of a given Boolean function to bent functions, investigate dependencies into the Walsh – Hadamard spectra, obtain restrictions on the number of representations as sums of squares of integers bounded in magnitude.
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