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On plateaued functions, linear structures and permutation polynomials
Date
2019-01-01
Author
Mesnager, Sihem
Kaytancı, Kübra
Özbudak, Ferruh
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some applications of our new notion of linear translator to the construction of permutation polynomials. Furthermore, we give explicit classes of permutation polynomials over Fqn using some properties of Fq and some conditions of 2011, Akbary, Ghioca and Wang.
Subject Keywords
Plateaued functions
,
Permutation polynomials
,
Linear structure
URI
https://hdl.handle.net/11511/41074
DOI
https://doi.org/10.1007/978-3-030-16458-4_13
Collections
Graduate School of Applied Mathematics, Conference / Seminar
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S. Mesnager, K. Kaytancı, and F. Özbudak, “On plateaued functions, linear structures and permutation polynomials,” 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41074.