Abstract
We characterize bent functions and plateaued functions in terms of moments of their Walsh transforms. We introduce in any characteristic the notion of directional difference and establish a link between the fourth moment and that notion. We show that this link allows to identify bent elements of particular families. Notably, we characterize bent functions of algebraic degree \(3\).
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Mesnager, S. (2014). Characterizations of Plateaued and Bent Functions in Characteristic \(p\) . In: Schmidt, KU., Winterhof, A. (eds) Sequences and Their Applications - SETA 2014. SETA 2014. Lecture Notes in Computer Science(), vol 8865. Springer, Cham. https://doi.org/10.1007/978-3-319-12325-7_6
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DOI: https://doi.org/10.1007/978-3-319-12325-7_6
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