Negabent Boolean functions are defined by having a flat magnitude spectrum under the nega-Hadamard transform. They exist in both even and odd dimensions, and the subclass of functions that are simultaneously bent and negabent (bent-negabent) has attracted interest due to the combined optimal periodic and negaperiodic spectral properties. In this work, we investigate how evolutionary algorithms can be used to evolve (bent-)negabent Boolean functions. Our experimental results indicate that evolutionary algorithms, especially genetic programming, are a suitable approach for evolving negabent Boolean functions, and we successfully evolve such functions in all dimensions we consider.
@article{arxiv.2602.00843,
title = {NegaBent, No Regrets: Evolving Spectrally Flat Boolean Functions},
author = {Claude Carlet and Marko Ðurasevic and Ermes Franch and Domagoj Jakobovic and Luca Mariot and Stjepan Picek},
journal= {arXiv preprint arXiv:2602.00843},
year = {2026}
}