On the existence and non-existence of some classes of bent–negabent functions
| Autor: | Pantelimon Stanica, Bimal Mandal, Subhamoy Maitra |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Algebra and Number Theory Applied Mathematics Bent molecular geometry 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Function (mathematics) 01 natural sciences Prime (order theory) Combinatorics Symmetric function 010201 computation theory & mathematics Domain (ring theory) Theory of computation 0202 electrical engineering electronic engineering information engineering Rotation (mathematics) Mathematics |
| Zdroj: | Applicable Algebra in Engineering, Communication and Computing. 33:237-260 |
| ISSN: | 1432-0622 0938-1279 |
| DOI: | 10.1007/s00200-020-00444-w |
| Popis: | In this paper we investigate different questions related to bent–negabent functions. We first take an expository look at the state-of-the-art research in this domain and point out some technical flaws in certain results and fix some of them. Further, we derive a necessary and sufficient condition for which the functions of the form $${\mathbf{x}}\cdot \pi ({\mathbf{y}})\oplus h({\mathbf{y}})$$ [Maiorana–McFarland ( $${\mathcal {M}}$$ )] is bent–negabent, and more generally, we study the non-existence of bent–negabent functions in the $${\mathcal {M}}$$ class. We also identify some functions that are bent–negabent. Next, we continue the recent work by Mandal et al. (Discrete Appl Math 236:1–6, 2018) on rotation symmetric bent–negabent functions and show their non-existence in larger classes. For example, we prove that there is no rotation symmetric bent–negabent function in $$4p^k$$ variables, where p is an odd prime. We present the non-existence of such functions in certain classes that are affine transformations of rotation symmetric functions. Keeping in mind the existing literature, we correct here some technical issues and errors found in other papers and provide some novel results. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink