An Upper Bound on the Number of Bent Functions

TL;DR

This paper establishes an upper bound on the number of n-ary bent functions, showing it grows slower than previously estimated as n increases, providing new insights into their combinatorial limits.

Contribution

It introduces a tighter upper bound on the count of n-ary bent functions for even n, advancing understanding of their asymptotic behavior.

Findings

Number of n-ary bent functions is less than 2^{3·2^{n-3}(1+o(1))} for large even n

Provides asymptotic growth rate of bent functions

Refines previous bounds on bent function enumeration

Abstract

The number of $n$-ary bent functions is less than $2^{3\cdot2^{n-3}(1+o(1))}$ as $n$ is even and $n\rightarrow\infty$. Keywords: Boolean function, bent function, upper bound