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Applicable Algebra in Engineering, Communication and Computing

25-11-2024 | Original Paper

More constructions of permutation pentanomials and hexanomials over \(\mathbb {F}_{p^{2m}}\)

Authors: Ruihua Shen, Xianping Liu, Xiaofang Xu

Published in: Applicable Algebra in Engineering, Communication and Computing

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Abstract

In this paper, two classes of permutation pentanomials over finite fields \(\mathbb {F}_{p^{2m}}\) are investigated by transforming the permutation property of polynomials to verifying that some low-degree equations has no solutions in the unit circle. Furthermore, based on the study of the algebraic curves for fractional polynomials, several classes of permutation pentanomials and hexanomials over \(\mathbb {F}_{5^{2m}}\) are discovered. Additionally, we obtain some new permutation pentanomials, quadrinomials and octonomials over \(\mathbb {F}_{5^{2m}}\) from known permutation polynomials in the unit circle.

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Metadata
Title
More constructions of permutation pentanomials and hexanomials over
Authors
Ruihua Shen
Xianping Liu
Xiaofang Xu
Publication date
25-11-2024
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-024-00673-3

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