Plateaued Functions

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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.

Constructions of Boolean plateaued functions

Primary constructons

Maiorana-MacFarland Functions