Permutation polynomials of finite fields of even characteristic from character sums
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911028580712448 |
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| author | Chen, Ruikai Mesnager, Sihem |
| author_facet | Chen, Ruikai Mesnager, Sihem |
| contents | In this paper, we investigate permutation polynomials over the finite field $\mathbb F_{q^n}$ with $q=2^m$, focusing on those in the form $\mathrm{Tr}(Ax^{q+1})+L(x)$, where $A\in\mathbb F_{q^n}^*$ and $L$ is a $2$-linear polynomial over $\mathbb F_{q^n}$. By calculating certain character sums, we characterize these permutation polynomials and provide additional constructions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_15322 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Permutation polynomials of finite fields of even characteristic from character sums Chen, Ruikai Mesnager, Sihem Number Theory In this paper, we investigate permutation polynomials over the finite field $\mathbb F_{q^n}$ with $q=2^m$, focusing on those in the form $\mathrm{Tr}(Ax^{q+1})+L(x)$, where $A\in\mathbb F_{q^n}^*$ and $L$ is a $2$-linear polynomial over $\mathbb F_{q^n}$. By calculating certain character sums, we characterize these permutation polynomials and provide additional constructions. |
| title | Permutation polynomials of finite fields of even characteristic from character sums |
| topic | Number Theory |
| url | https://arxiv.org/abs/2406.15322 |