Bent functions construction using extended Maiorana-McFarland's class

In a particular case, we consider the extended Maiorana-McFarland class to obtain bent functions with balance in its images, restricted to vectors with even Hamming weight. Additionally, we see that all bent functions are balanced when we restrict to vectors of even Hamming weight or to vectors with odd Hamming weight. Given the necessary tools, we provide a simpler algorithm to obtain new bent functions using Maiorana-McFarland.