Local permutation polynomials of maximum degree over prime finite fields
Let q be a power of a prime p, Fq be the finite field with q elements, and Fq[x1,…,xn] be the ring of polynomials in n variables over Fq. The construction and study of local permutation polynomials of Fq[x1,…,xn] is recently increasing interest among the experts. In this work, we study local permuta...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/36810 |
| Acceso en línea: | https://hdl.handle.net/10902/36810 |
| Access Level: | acceso abierto |
| Palabra clave: | Permutation polynomials Local permutation polynomials Finite fields Multivariate polynomials ring |
| Sumario: | Let q be a power of a prime p, Fq be the finite field with q elements, and Fq[x1,…,xn] be the ring of polynomials in n variables over Fq. The construction and study of local permutation polynomials of Fq[x1,…,xn] is recently increasing interest among the experts. In this work, we study local permutation polynomials of maximum degree n(q−2) defined over the prime finite field Fp. In particular, we explicitly construct families of such polynomials when p≥5 and n≤p−1; and for any q of the form q=ppr when r≥1 and p≥3. |
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