Some permutation pentanomials over finite fields of even characteristic
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917873977393152 |
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| author | Kousar, Farhana Xiong, Maosheng |
| author_facet | Kousar, Farhana Xiong, Maosheng |
| contents | In a recent paper Zhang et al. constructed 17 families of permutation pentanomials of the form $x^t+x^{r_1(q-1)+t}+x^{r_2(q-1)+t}+x^{r_3(q-1)+t}+x^{r_4(q-1)+t}$ over $\mathbb{F}_{q^2}$ where $q=2^m$. In this paper for 14 of these 17 families we provide a simple explanation as to why they are permutations. We also extend these 14 families into three general classes of permutation pentanomials over $\mathbb{F}_{q^2}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_14641 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some permutation pentanomials over finite fields of even characteristic Kousar, Farhana Xiong, Maosheng Combinatorics Discrete Mathematics Number Theory In a recent paper Zhang et al. constructed 17 families of permutation pentanomials of the form $x^t+x^{r_1(q-1)+t}+x^{r_2(q-1)+t}+x^{r_3(q-1)+t}+x^{r_4(q-1)+t}$ over $\mathbb{F}_{q^2}$ where $q=2^m$. In this paper for 14 of these 17 families we provide a simple explanation as to why they are permutations. We also extend these 14 families into three general classes of permutation pentanomials over $\mathbb{F}_{q^2}$. |
| title | Some permutation pentanomials over finite fields of even characteristic |
| topic | Combinatorics Discrete Mathematics Number Theory |
| url | https://arxiv.org/abs/2412.14641 |