Abstract
A Boolean function with an even number of variables is called bent if it is maximally nonlinear. This paper extends the recent work of the author on bent functions (“Several new infinite families of bent functions and their duals”, IEEE-IT, 60(7), pp. 4397-4407, 2014). We exhibit several new infinite families of bent functions with their dual (bent) functions. Some of them are obtained via new infinite families of permutations that we provide with their compositional inverses. We introduce secondary-like constructions of permutations leading to the construction of several families of bent functions.
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Notes
A Boolean function g on \({\mathbb {F}_{2^{m}}}\) is said to be balanced if its Hamming weight w t(g) equals 2m−1 where w t(g) is the cardinality of its support \(supp(g):=\{x\in {\mathbb {F}_{2^{m}}} \mid g(x)=1\}.\)
The Maiorana-McFarland completed class is the smallest possible complete class containing the class of Maiorana-McFarland which is globally invariant under the action of the general affine group and under the addition of affine functions.
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Mesnager, S. Further constructions of infinite families of bent functions from new permutations and their duals. Cryptogr. Commun. 8, 229–246 (2016). https://doi.org/10.1007/s12095-015-0144-7
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DOI: https://doi.org/10.1007/s12095-015-0144-7