Further results on permutation polynomials and complete permutation polynomials over finite fields
In this paper, by employing the AGW criterion and determining the number of solutions to some equations over finite fields, we further investigate nine classes of permutation polynomials over $ \mathbb{F}_{p^n} $ with the form $ (x^{p^m}-x+\delta)^{s_1}+(x^{p^m}-x+\delta)^{s_2}+x $ and propose five...
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AIMS Press
2021-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021783?viewType=HTML |
| _version_ | 1823935077391794176 |
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| author | Qian Liu Jianrui Xie Ximeng Liu Jian Zou |
| author_facet | Qian Liu Jianrui Xie Ximeng Liu Jian Zou |
| author_sort | Qian Liu |
| collection | DOAJ |
| description | In this paper, by employing the AGW criterion and determining the number of solutions to some equations over finite fields, we further investigate nine classes of permutation polynomials over $ \mathbb{F}_{p^n} $ with the form $ (x^{p^m}-x+\delta)^{s_1}+(x^{p^m}-x+\delta)^{s_2}+x $ and propose five classes of complete permutation polynomials over $ \mathbb{F}_{p^{2m}} $ with the form $ ax^{p^m}+bx+h(x^{p^m}-x) $. |
| first_indexed | 2024-12-16T22:30:31Z |
| format | Article |
| id | doaj.art-499901e87d054b2e8814948c3a7a822a |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-16T22:30:31Z |
| publishDate | 2021-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-499901e87d054b2e8814948c3a7a822a2022-12-21T22:13:46ZengAIMS PressAIMS Mathematics2473-69882021-09-01612135031351410.3934/math.2021783Further results on permutation polynomials and complete permutation polynomials over finite fieldsQian Liu0Jianrui Xie 1Ximeng Liu2Jian Zou31. College of Computer and Data Science, Fuzhou University, Fuzhou 350116, China 2. Key Laboratory of Information Security of Network Systems, Fuzhou University, Fuzhou 350116, China3. imec-COSIC, KU Leuven, Leuven, Belgium1. College of Computer and Data Science, Fuzhou University, Fuzhou 350116, China 2. Key Laboratory of Information Security of Network Systems, Fuzhou University, Fuzhou 350116, China1. College of Computer and Data Science, Fuzhou University, Fuzhou 350116, China 2. Key Laboratory of Information Security of Network Systems, Fuzhou University, Fuzhou 350116, ChinaIn this paper, by employing the AGW criterion and determining the number of solutions to some equations over finite fields, we further investigate nine classes of permutation polynomials over $ \mathbb{F}_{p^n} $ with the form $ (x^{p^m}-x+\delta)^{s_1}+(x^{p^m}-x+\delta)^{s_2}+x $ and propose five classes of complete permutation polynomials over $ \mathbb{F}_{p^{2m}} $ with the form $ ax^{p^m}+bx+h(x^{p^m}-x) $.https://www.aimspress.com/article/doi/10.3934/math.2021783?viewType=HTMLfinite fieldagw criterionpermutation polynomialcomplete permutation polynomial |
| spellingShingle | Qian Liu Jianrui Xie Ximeng Liu Jian Zou Further results on permutation polynomials and complete permutation polynomials over finite fields AIMS Mathematics finite field agw criterion permutation polynomial complete permutation polynomial |
| title | Further results on permutation polynomials and complete permutation polynomials over finite fields |
| title_full | Further results on permutation polynomials and complete permutation polynomials over finite fields |
| title_fullStr | Further results on permutation polynomials and complete permutation polynomials over finite fields |
| title_full_unstemmed | Further results on permutation polynomials and complete permutation polynomials over finite fields |
| title_short | Further results on permutation polynomials and complete permutation polynomials over finite fields |
| title_sort | further results on permutation polynomials and complete permutation polynomials over finite fields |
| topic | finite field agw criterion permutation polynomial complete permutation polynomial |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021783?viewType=HTML |
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