New permutation polynomials over $\mathbb{F}_{q^2}$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908628142784512 |
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| author | Pang, Xuan Yuan, Pingzhi Wu, Danyao Guan, Huanhuan |
| author_facet | Pang, Xuan Yuan, Pingzhi Wu, Danyao Guan, Huanhuan |
| contents | In this paper, we propose a new method to obtain new permutation polynomials over $\mathbb{F}_{q^2}$. Using this method, we extend many known permutation polynomials, which take the form $\sum_i(x^q-x+δ)^{s_i}+L(x)$, where $L(x)$ is a $q$-polynomial over $\mathbb{F}_q$ and $δ\in\mathbb{F}_{q^2}$. We also present an alternative approach for constructing permutation polynomials of the form $x+γTr_q^{q^d}(x^{q+1}+x^{2q+2})$ for the cases where $q=2^m$, $2\nmid d$ and $ Tr_q^{q^d}(x)=x+x^q+\dots+x^{q^{d-1}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_02616 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New permutation polynomials over $\mathbb{F}_{q^2}$ Pang, Xuan Yuan, Pingzhi Wu, Danyao Guan, Huanhuan Number Theory 11T06 In this paper, we propose a new method to obtain new permutation polynomials over $\mathbb{F}_{q^2}$. Using this method, we extend many known permutation polynomials, which take the form $\sum_i(x^q-x+δ)^{s_i}+L(x)$, where $L(x)$ is a $q$-polynomial over $\mathbb{F}_q$ and $δ\in\mathbb{F}_{q^2}$. We also present an alternative approach for constructing permutation polynomials of the form $x+γTr_q^{q^d}(x^{q+1}+x^{2q+2})$ for the cases where $q=2^m$, $2\nmid d$ and $ Tr_q^{q^d}(x)=x+x^q+\dots+x^{q^{d-1}}$. |
| title | New permutation polynomials over $\mathbb{F}_{q^2}$ |
| topic | Number Theory 11T06 |
| url | https://arxiv.org/abs/2511.02616 |