2011
DOI: 10.1134/s1990478911010133
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Generalizations of bent functions. A survey

Abstract: Bent functions (Boolean functions with extreme nonlinearity properties) are actively studied for their numerous applications in cryptography, coding theory, and other fields. New statements of problems lead to a large number of generalizations of the bent functions many of which remain little known to the experts in Boolean functions. In this article, we offer a systematic survey of them.

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Cited by 47 publications
(16 citation statements)
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“…Their definitions are given in the follows. We can see more results about the constructions of bent functions and near bent functions in the papers [14][15].…”
Section: Similar-bent Functionmentioning
confidence: 99%
“…Their definitions are given in the follows. We can see more results about the constructions of bent functions and near bent functions in the papers [14][15].…”
Section: Similar-bent Functionmentioning
confidence: 99%
“…One of the simplest examples is Rothaus's bent function f (x) = x 1 x 2 + x 3 x 4 + · · · + x 2t−1 x 2t , where n = 2t. For m = 4 and m = 8, several constructions and existence results on GBFs have been found in [5,[8][9][10][11][12][13]. Generalized bent functions have been widely investigated since they are applied in many fields such as communication theory, cryptography and closely related to coding theory and combinatorial design theory.…”
Section: Introductionmentioning
confidence: 99%
“…A function with minimum absolute WHT values is called q-ary bent, i.e. f ∈ B n,q is q-ary bent if |W f (u)| = q n/2 for every u ∈ Z n q [9,11,15].…”
Section: Preliminariesmentioning
confidence: 99%