# Plateaued Functions

## Contents

# Background and Definition

A Boolean function is said to be *plateaued* if its Walsh transform takes at most three distinct values, viz. and for some positive ineger called the *amplitude* of .

This notion can be naturally extended to vectorial Boolean functions by applying it to each component. More precisely, if is an -function, we say that is *plateaued* if all its component functions for are plateaued. If all of the component functions are plateaued and have the same amplitude, we say that is *plateaued with single amplitude*.

## Equivalence relations

The class of functions that are plateaued with single amplitude is CCZ-invariant.

The class of plateaued functions is only EA-invariant.

## Relations to other classes of functions

All bent and semi-bent Boolean functions are plateaued.

Any vectorial AB function is plateaued with single amplitude.