Article Contents

2024, Volume 18, Issue 6: 1681-1689. Doi: 10.3934/amc.2023014

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Boolean function classes with high nonlinearity

Kezia Saini and
Manish Garg^,

Department of Mathematics, The LNM Institute of Information Technology, Jaipur 302031, India

^*Corresponding author: Manish Garg
^*Corresponding author: Manish Garg

Received: December 2022

Revised: April 2023

Early access: April 2023

Published: December 2024

The first author is supported by [Council of Scientific and Industrial Research (CSIR)]

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Abstract

In 2020, Liu (Q. Liu, The lower bounds on the second-order nonlinearity of three classes of Boolean functions, Advances in Mathematics of Communications, AIMS (2021), Doi: 10.3934/amc.2020136) studied the second-order nonlinearity of three classes of Boolean functions, which have high first-order nonlinearity. Liu gave bounds on the first-order nonlinearity of these classes based on some experimental results using Magma. This article provides theoretical proof for computing the lower bounds on the first-order nonlinearity of two classes of Boolean functions out of three. Our bounds are identical to the bounds obtained by Liu experimentally.

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Mathematics Subject Classification: Primary: 94A60, 94D10; Secondary: 06E30.

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