Abstract
Bent functions are maximally nonlinear Boolean functions. They are wonderful creatures introduced by O. Rothaus in the 1960’s and studied firstly by J. Dillon since 1974. Using some involutions over finite fields, we present new constructions of bent functions in the line of recent Mesnager’s works. One of the constructions is based on an arithmetical problem. We discuss existence of such bent functions using Fermat hypersurface and Lang-Weil estimations.
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Mesnager, S., Cohen, G., & Madore, D. (2015). On existence (Based on an arithmetical problem) and constructions of bent functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9496, pp. 3–19). Springer Verlag. https://doi.org/10.1007/978-3-319-27239-9_1
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