On plateaued functions, linear structures and permutation polynomials

2019-01-01
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.

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Citation Formats
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.