An asymptotic lower bound on the number of bent functions

Abstract

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.

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

References in corpus (2)

• A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity
• An Upper Bound on the Number of Bent Functions

Cited by in corpus (1)

• Constructing MRD codes by switching