Four new classes of permutation trinomials and their compositional inverses
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910927762227200 |
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| author | Hasan, Sartaj Ul Kaur, Ramandeep Kumar, Hridesh |
| author_facet | Hasan, Sartaj Ul Kaur, Ramandeep Kumar, Hridesh |
| contents | We construct four new classes of permutation trinomials over the cubic extension of a finite field with even characteristic. Additionally, we explicitly provide the compositional inverse of each class of permutation trinomials in polynomial form. Furthermore, we derive the compositional inverse of the permutation trinomial $αX^{q(q^2 - q + 1)} + βX^{q^2 - q + 1} + 2X$ for $α= 1$ and $β= 1$, originally proposed by Xie, Li, Xu, Zeng, and Tang (2023). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Four new classes of permutation trinomials and their compositional inverses Hasan, Sartaj Ul Kaur, Ramandeep Kumar, Hridesh Number Theory We construct four new classes of permutation trinomials over the cubic extension of a finite field with even characteristic. Additionally, we explicitly provide the compositional inverse of each class of permutation trinomials in polynomial form. Furthermore, we derive the compositional inverse of the permutation trinomial $αX^{q(q^2 - q + 1)} + βX^{q^2 - q + 1} + 2X$ for $α= 1$ and $β= 1$, originally proposed by Xie, Li, Xu, Zeng, and Tang (2023). |
| title | Four new classes of permutation trinomials and their compositional inverses |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.02128 |