Secondary constructions of (non)weakly regular plateaued functions over finite fields

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2021-01-01

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Mesnager, Sihem
Özbudak, Ferruh
Sinak, Ahmet

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Plateaued (vectorial) functions over finite fields have diverse applications in symmetric cryptography, coding theory, and sequence theory. Constructing these functions is an attractive research topic in the literature. We can distinguish two kinds of constructions of plateaued functions: secondary constructions and primary constructions. The first method uses already known functions to obtain new functions while the latter do not need to use previously constructed functions to obtain new functions. In this work, the first secondary constructions of (non)weakly regular plateaued (vectorial) functions are presented over the finite fields of odd characteristics. We also introduce some recursive constructions of (non)weakly regular plateaued p-ary functions by using already known such functions. We obtain nontrivial plateaued functions from the previously known trivial plateaued (partially bent) functions in the proposed construction methods.

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https://hdl.handle.net/11511/93707

Journal

TURKISH JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.3906/mat-2104-5

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Department of Mathematics, Article

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Citation Formats

S. Mesnager, F. Özbudak, and A. Sinak, “Secondary constructions of (non)weakly regular plateaued functions over finite fields,” TURKISH JOURNAL OF MATHEMATICS, vol. 45, pp. 2295–2306, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/93707.