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Published in: Applicable Algebra in Engineering, Communication and Computing 2/2023

10-04-2021 | Original Paper

Constructing permutation trinomials via monomials on the subsets of \(\mu _{q+1}\)

Authors: Xiaoer Qin, Li Yan

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 2/2023

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Abstract

Constructing permutation polynomials is a hot topic in finite fields, and permutation polynomials have many applications in different areas. Recently, several classes of permutation trinomials with index \(q+1\) over \(\mathbf{F}_{q^2}\) were constructed. In this paper, we mainly construct permutation trinomials with index \(q+1\) over \(\mathbf{F}_{q^2}\). By using monomials of \(\mu _{(q+1)/2}\) and \(-\mu _{(q+1)/2}\) to study the permutational property of \(x^rh(x)^{q-1}\) on \(\mu _{q+1}\), we characterize many kinds of permutation trinomials of the form \(x^rh(x^{q-1})\) over \(\mathbf{F}_{q^{2}}\). Furthermore, by using a similar method, we show several classes of permutation trinomials with index \(q+1\) over \(\mathbf{F}_{2^{2k}}\) with k being odd.

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Metadata
Title
Constructing permutation trinomials via monomials on the subsets of
Authors
Xiaoer Qin
Li Yan
Publication date
10-04-2021
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 2/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-021-00505-8

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