Small Primitive Normal Elements in Finite Fields
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912802286862336 |
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| author | Carella, N. A. |
| author_facet | Carella, N. A. |
| contents | Let $q=p^k$ be a prime power, let $\mathbb{F}_q$ be a finite field and let $n\geq2$ be an integer. This note investigates the existence small primitive normal elements in finite field extensions $\mathbb{F}_{q^n}$. It is shown that a small nonstructured subset $\mathcal{A}\subset \mathbb{F}_{q^n}$ of cardinality $\#\mathcal{A}\gg (\log q^n) (\log\log q^n)^{1+\varepsilon}) $, where $\varepsilon>0$ is a small number, contains a primitive normal element. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Small Primitive Normal Elements in Finite Fields Carella, N. A. General Mathematics Primary 11T30, 12E20, Secondary 11N37 Let $q=p^k$ be a prime power, let $\mathbb{F}_q$ be a finite field and let $n\geq2$ be an integer. This note investigates the existence small primitive normal elements in finite field extensions $\mathbb{F}_{q^n}$. It is shown that a small nonstructured subset $\mathcal{A}\subset \mathbb{F}_{q^n}$ of cardinality $\#\mathcal{A}\gg (\log q^n) (\log\log q^n)^{1+\varepsilon}) $, where $\varepsilon>0$ is a small number, contains a primitive normal element. |
| title | Small Primitive Normal Elements in Finite Fields |
| topic | General Mathematics Primary 11T30, 12E20, Secondary 11N37 |
| url | https://arxiv.org/abs/2504.21007 |