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Bibliographic Details
Main Authors: Potapov, V. N., Taranenko, A. A., Tarannikov, Yu. V.
Format: Preprint
Published: 2021
Subjects:
Online Access:https://arxiv.org/abs/2108.00232
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Table of Contents:
  • A Boolean function $f$ on $n$ variables is said to be a bent function if the absolute value of all its Walsh coefficients is $2^{n/2}$. Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on a modification of the Maiorana--McFarland family of bent functions and recent progress in the estimation of the number of transversals in latin squares and hypercubes. By-products of our proofs are the asymptotics of the logarithm of the numbers of partitions of the Boolean hypercube into $2$-dimensional affine and linear subspaces.