The compositional inverses of permutation polynomials from trace functions over finite fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912051374325760 |
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| author | Wu, Danyao Yuan, Pingzhi |
| author_facet | Wu, Danyao Yuan, Pingzhi |
| contents | In this paper, we present the compositional inverses of several classes permutation polynomials of the form $\sum_{i=1}^kb_i\left({\rm Tr}_m^{mn}(x)^{t_i}+δ\right)^{s_i}+f_1(x)$, where $1\leq i \leq k,$ $s_i$ are positive integers, $b_i \in \mathbb{F}_{p^m},$ $p$ is a prime and $f_1(x)$ is a polynomial over $\mathbb{F}_{p^{mn}}$ satisfying the following conditions:
(i) ${\rm Tr}_m^{mn}(x) \circ f_1(x)=φ(x) \circ {\rm Tr}_m^{mn}(x),$ where $φ(x)$ is a polynomial over $\mathbb{F}_{p^m};$
(ii) For any $a \in \mathbb{F}_{p^m},$ $f_1(x)$ is injective on ${\rm Tr}_m^{mn}(a)^{-1}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The compositional inverses of permutation polynomials from trace functions over finite fields Wu, Danyao Yuan, Pingzhi Number Theory In this paper, we present the compositional inverses of several classes permutation polynomials of the form $\sum_{i=1}^kb_i\left({\rm Tr}_m^{mn}(x)^{t_i}+δ\right)^{s_i}+f_1(x)$, where $1\leq i \leq k,$ $s_i$ are positive integers, $b_i \in \mathbb{F}_{p^m},$ $p$ is a prime and $f_1(x)$ is a polynomial over $\mathbb{F}_{p^{mn}}$ satisfying the following conditions: (i) ${\rm Tr}_m^{mn}(x) \circ f_1(x)=φ(x) \circ {\rm Tr}_m^{mn}(x),$ where $φ(x)$ is a polynomial over $\mathbb{F}_{p^m};$ (ii) For any $a \in \mathbb{F}_{p^m},$ $f_1(x)$ is injective on ${\rm Tr}_m^{mn}(a)^{-1}.$ |
| title | The compositional inverses of permutation polynomials from trace functions over finite fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2409.20000 |