Paper 2024/413

Bent functions construction using extended Maiorana-McFarland’s class

Abstract

We use the extended Maiorana-McFarland's class to obtain bent functions. Additionally, we obtain balanced functions when we restrict its domain to vectors with even Hamming weight, i.e., an equal number of pre-images for 0 and 1. We have defined a bent function on an affine space to achieve this. Additionally, we demonstrate that the bent functions, in general, are balanced by restricting them to vectors of even Hamming or odd Hamming weight. Since that we have all the necessary tools, we present an algorithm for generating new bent functions of any dimension using the Maiorana-McFarland approach multiple times.