Several classes of permutation polynomials of the form (xpm − x + δ)s + x over Fp2m
In this paper, we give a further study on the permutation behavior of polynomials of a special form by considering the number of solutions of certain equations over finite fields. First, four classes of permutation polynomials of the form (x2m+x+δ)s+x over F22m are presented. Notably, some necessary...
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sg-ntu-dr.10356-1556612023-02-28T19:56:55Z Several classes of permutation polynomials of the form (xpm − x + δ)s + x over Fp2m Xu, Guangkui Luo, Gaojun Cao, Xiwang School of Physical and Mathematical Sciences Science::Mathematics::Algebra Finite Field Permutation Polynomial In this paper, we give a further study on the permutation behavior of polynomials of a special form by considering the number of solutions of certain equations over finite fields. First, four classes of permutation polynomials of the form (x2m+x+δ)s+x over F22m are presented. Notably, some necessary and sufficient conditions for this kind of polynomials to permute F22m are provided. Second, we present several classes of permutation polynomials of the form (xpm−x+δ)s+x over Fp2m of odd characteristic, some of which can provide complete permutation polynomials of this form over F32m. Nanyang Technological University Submitted/Accepted version G. Xu was supported by the National Natural Science Foundation of China (Grant No. 62172183), the Natural Science Foundation for the Higher Education Institutions of Anhui Province of China under Grant KJ2020A0643 and Program for Innovative Research Team in Huainan Normal University (XJTD202008). G. Luo was supported by Nanyang Technological University Research Grant No. 04INS000047C230GRT01. X. Cao was supported by the National Natural Science Foundation of China (Grant No. 12171241). 2022-03-11T08:25:03Z 2022-03-11T08:25:03Z 2022 Journal Article Xu, G., Luo, G. & Cao, X. (2022). Several classes of permutation polynomials of the form (xpm − x + δ)s + x over Fp2m. Finite Fields and Their Applications, 79, 102001-. https://dx.doi.org/10.1016/j.ffa.2022.102001 1071-5797 https://hdl.handle.net/10356/155661 10.1016/j.ffa.2022.102001 2-s2.0-85123872960 79 102001 en 04INS000047C230GRT01 Finite Fields and Their Applications © 2022 Elsevier Inc. All rights reserved. This paper was published in Finite Fields and Their Applications and is made available with permission of Elsevier Inc. application/pdf |
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Science::Mathematics::Algebra Finite Field Permutation Polynomial Xu, Guangkui Luo, Gaojun Cao, Xiwang Several classes of permutation polynomials of the form (xpm − x + δ)s + x over Fp2m |
| description |
In this paper, we give a further study on the permutation behavior of polynomials of a special form by considering the number of solutions of certain equations over finite fields. First, four classes of permutation polynomials of the form (x2m+x+δ)s+x over F22m are presented. Notably, some necessary and sufficient conditions for this kind of polynomials to permute F22m are provided. Second, we present several classes of permutation polynomials of the form (xpm−x+δ)s+x over Fp2m of odd characteristic, some of which can provide complete permutation polynomials of this form over F32m. |
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School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Xu, Guangkui Luo, Gaojun Cao, Xiwang |
| format |
Article |
| author |
Xu, Guangkui Luo, Gaojun Cao, Xiwang |
| author_sort |
Xu, Guangkui |
| title |
Several classes of permutation polynomials of the form (xpm − x + δ)s + x over Fp2m |
| title_short |
Several classes of permutation polynomials of the form (xpm − x + δ)s + x over Fp2m |
| title_full |
Several classes of permutation polynomials of the form (xpm − x + δ)s + x over Fp2m |
| title_fullStr |
Several classes of permutation polynomials of the form (xpm − x + δ)s + x over Fp2m |
| title_full_unstemmed |
Several classes of permutation polynomials of the form (xpm − x + δ)s + x over Fp2m |
| title_sort |
several classes of permutation polynomials of the form (xpm − x + δ)s + x over fp2m |
| publishDate |
2022 |
| url |
https://hdl.handle.net/10356/155661 |
| _version_ |
1759852944400842752 |