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Crooked functions

Abstract : Crooked permutations were introduced twenty years ago since they allow to construct interesting objects in graph theory. The field of applications was extended later. Crooked functions, bijective or not, correspond to APN functions and to some optimal codes. We adopt an unified presentation of crooked functions, explaining the connection with partially-bent functions. We then complete some known results and derive new properties. For instance, we observe that crooked functions allow to construct sets of bent functions and define some permutations.
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https://hal.inria.fr/hal-02969132
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Submitted on : Friday, October 16, 2020 - 1:22:14 PM
Last modification on : Monday, February 8, 2021 - 8:35:38 PM

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Pascale Charpin. Crooked functions. Proceedings of the 14th International Conference on Finite Fields and their Applications, Jun 2021, Vancouver, Canada. pp.87-102, ⟨10.1515/9783110621730-007⟩. ⟨hal-02969132⟩

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