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Applicable Algebra in Engineering, Communication and Computing

13.05.2024 | Original Paper

New results of sparse permutation polynomials with trace functions over \(\mathbb {F}_{q^n}\)

verfasst von: Yan-Ping Wang, Zhengbang Zha

Erschienen in: Applicable Algebra in Engineering, Communication and Computing

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Abstract

Permutation polynomials with sparse forms over finite fields attract researchers’ great interest and have important applications in many areas of mathematics and engineering. In this paper, by investigating the exponents (s, i) and the coefficients \(a,b\in \mathbb {F}_{q}^{*}\), we present some new results of permutation polynomials of the form \(f(x)= ax^{q^i(q^{2}-q+1)} + bx^{s} + \textrm{Tr}_{q^n/q}(x)\) over \(\mathbb {F}_{q^n}\) (\(n=2\) or 3). The permutation property of the new results is given by studying the number of solutions of special equations over \(\mathbb {F}_{q^n}\).

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Titel: New results of sparse permutation polynomials with trace functions over
verfasst von: Yan-Ping Wang
Zhengbang Zha
Publikationsdatum: 13.05.2024
Verlag: Springer Berlin Heidelberg
Erschienen in: Applicable Algebra in Engineering, Communication and Computing
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-024-00658-2

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