Relation between o-equivalence and EA-equivalence for Niho bent functions |
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Affiliation: | 1. Department of Informatics, University of Bergen, PB 7803, N-5020 Bergen, Norway;2. Department of Mathematics, Universities of Paris 8 and Paris 13, 2 rue de la liberté, 93526 Saint-Denis Cedex, France;3. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium;4. School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005, Australia |
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Abstract: | Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent functions, so-called Niho bent functions there is a more general equivalence relation called o-equivalence which is induced from the equivalence of o-polynomials. In the present work we study, for a given o-polynomial, a general construction which provides all possible o-equivalent Niho bent functions, and we considerably simplify it to a form which excludes EA-equivalent cases. That is, we identify all cases which can potentially lead to pairwise EA-inequivalent Niho bent functions derived from o-equivalence of any given Niho bent function. Furthermore, we determine all pairwise EA-inequivalent Niho bent functions arising from all known o-polynomials via o-equivalence. |
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Keywords: | Bent function Boolean function EA-equivalence Maximum nonlinearity Modified Magic action Niho bent function o-Equivalence o-Polynomials Ovals Hyperovals |
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