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Equivalence classes of Niho bent functions

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Abstract

Equivalence classes of Niho bent functions are in one-to-one correspondence with equivalence classes of ovals in a projective plane. Since a hyperoval can produce several ovals, each hyperoval is associated with several inequivalent Niho bent functions. For all known types of hyperovals we described the equivalence classes of the corresponding Niho bent functions. For some types of hyperovals the number of equivalence classes of the associated Niho bent functions are at most 4. In general, the number of equivalence classes of associated Niho bent functions increases exponentially as the dimension of the underlying vector space grows. In small dimensions the equivalence classes were considered in detail.

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Acknowledgements

The author would like to thank Sihem Mesnager and Alexander Pott for valuable discussions. The author is also grateful to the anonymous reviewers for their detailed comments that improved the presentation and quality of this paper.

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    Kanat Abdukhalikov

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Correspondence to Kanat Abdukhalikov.

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Communicated by A. Pott.

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Abdukhalikov, K. Equivalence classes of Niho bent functions. Des. Codes Cryptogr. 89, 1509–1534 (2021). https://doi.org/10.1007/s10623-021-00885-5

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