Non lin\'earit\'e des fonctions bool\'eennes donn\'ees par des traces de polyn\^omes de degr\'e binaire 3

TL;DR

This paper investigates the nonlinearity of Boolean functions over finite fields, specifically those derived from polynomials of degree 7 or higher, with a focus on functions over fields where the extension degree is odd.

Contribution

It provides new insights into the nonlinearity properties of Boolean functions associated with higher-degree polynomials over finite fields with odd extension degrees.

Findings

Analyzes nonlinearity of functions from degree 7 polynomials

Extends study to more general polynomial classes

Provides bounds or characterizations of nonlinearity

Abstract

Nous \'etudions la non lin\'earit\'e des fonctions d\'efinies sur F_{2^m} o\`u $m$ est un entier impair, associ\'ees aux polyn\^omes de degr\'e 7 ou \`a des polyn\^omes plus g\'en\'eraux. ----- We study the nonlinearity of the functions defined on F_{2^m} where $m$ is an odd integer, associated to the polynomials of degree 7 or more general polynomials.