Existence of balanced functions that are not derivative of bent functions

TL;DR

This paper disproves Tokareva's conjecture by showing that some balanced boolean functions are not derivatives of bent functions, using new upper bounds for bent and plateaued functions.

Contribution

It introduces new upper bounds for bent and plateaued functions, leading to the disproof of Tokareva's conjecture.

Findings

Disproved Tokareva's conjecture

Established new upper bounds for bent functions

Identified balanced functions not derivable from bent functions

Abstract

It is disproved the Tokareva's conjecture that any balanced boolean function of appropriate degree is a derivative of some bent function. This result is based on new upper bounds for the numbers of bent and plateaued functions.