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EA-inequivalence of bent functions

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Abstract

The question of establishing EA-inequivalence among the classes of bent functions remains in general an open problem. The EA-inequivalence is also relevant in classifying bent functions within the same class. This paper is an attempt to investigate these questions for the Maiorana–McFarland (\(\mathcal{M}\)) class and so-called class \(\mathcal{H}\) of bent functions. For cubic bent functions of the form \(Tr_1^t(xy^{2^i+1})\) in \(\mathcal{M}\), the necessary and sufficient conditions related to EA-equivalence are derived. It is also shown that in most of the cases, at least over finite fields of relatively small order, bent functions within \(\mathcal{H}\) are EA-inequivalent.

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Acknowledgements

The author would like to thank Sugata Gangopadhyay for several helpful discussions. Samed Bajrić is supported by the Slovenian Research Agency (Research Program P2-0037). The author would also like to thank the reviewers for all of their careful, constructive and insightful comments in relation to this work.

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Correspondence to Samed Bajrić.

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Bajrić, S. EA-inequivalence of bent functions. AAECC (2020). https://doi.org/10.1007/s00200-020-00418-y

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Keywords

  • Bent function
  • Affine equivalence
  • EA-equivalence
  • Derivatives

Mathematics Subject Classification

  • 68R01
  • 11T71
  • 94C10