Further Investigation on Cyclotomic Mapping Permutation Polynomials over Finite Fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909833792323584 |
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| author | Mondal, Suman |
| author_facet | Mondal, Suman |
| contents | We explore the connection between cyclotomic mapping permutation polynomials and permutation polynomials of the form $x^rf(x^{\frac{q-1}{l}})$ over finite fields. We present a new necessary and a new sufficient condition to verify permutation behavior of such polynomials over finite field. As its application, for particular values of $r$, we point out some permutation trinomials of the form $P(x)=2x^{r+8}+x^{r+4}+2x^r \in \mathbb{F}_{13}[x]$, and work on few classes of permutation binomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Further Investigation on Cyclotomic Mapping Permutation Polynomials over Finite Fields Mondal, Suman Number Theory 12E20, 11T06 We explore the connection between cyclotomic mapping permutation polynomials and permutation polynomials of the form $x^rf(x^{\frac{q-1}{l}})$ over finite fields. We present a new necessary and a new sufficient condition to verify permutation behavior of such polynomials over finite field. As its application, for particular values of $r$, we point out some permutation trinomials of the form $P(x)=2x^{r+8}+x^{r+4}+2x^r \in \mathbb{F}_{13}[x]$, and work on few classes of permutation binomials. |
| title | Further Investigation on Cyclotomic Mapping Permutation Polynomials over Finite Fields |
| topic | Number Theory 12E20, 11T06 |
| url | https://arxiv.org/abs/2510.08760 |