An asymptotic lower bound on the number of bent functions
Combinatorics
2024-10-29 v2
Abstract
A Boolean function on variables is said to be a bent function if the absolute value of all its Walsh coefficients is . 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 -dimensional affine and linear subspaces.
Keywords
Cite
@article{arxiv.2108.00232,
title = {An asymptotic lower bound on the number of bent functions},
author = {V. N. Potapov and A. A. Taranenko and Yu. V. Tarannikov},
journal= {arXiv preprint arXiv:2108.00232},
year = {2024}
}
Comments
v.1: 10 pages v.2: 13 pages; all main results remain the same, but we extend the introduction, add many references, change the title, and make a large number of other small improvements