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12-02-2020 | Original Paper

EA-inequivalence of bent functions

Author: Samed Bajrić

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 6/2021

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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Title: EA-inequivalence of bent functions
Author: Samed Bajrić
Publication date: 12-02-2020
Publisher: Springer Berlin Heidelberg
Published in: Applicable Algebra in Engineering, Communication and Computing / Issue 6/2021
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-020-00418-y

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