The compositional inverses of three classes of permutation polynomials over finite fields
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929543209549824 |
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| author | Wu, Danyao Yuan, Pingzhi |
| author_facet | Wu, Danyao Yuan, Pingzhi |
| contents | Recently, P. Yuan presented a local method to find permutation polynomials and their compositional inverses over finite fields. The work of P. Yuan inspires us to compute the compositional inverses of three classes of the permutation polynomials: (a) the permutation polynomials of the form $ax^q+bx+(x^q-x)^k$ over $\mathbb{F}_{q^2},$ where $a+b \in \mathbb{F}_q^*$ or $a^q=b;$ (b) the permutation polynomials of the forms $f(x)=-x+x^{(q^2+1)/2}+x^{(q^3+q)/2} $ and $f(x)+x$ over $\mathbb{F}_{q^3};$ (c) the permutation polynomial of the form $A^{m}(x)+L(x)$ over $\mathbb{F}_{q^n},$ where ${\rm Im}(A(x))$ is a vector space with dimension $1$ over $\mathbb{F}_{q}$ and $L(x)$ is not a linearized permutation polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The compositional inverses of three classes of permutation polynomials over finite fields Wu, Danyao Yuan, Pingzhi Number Theory Recently, P. Yuan presented a local method to find permutation polynomials and their compositional inverses over finite fields. The work of P. Yuan inspires us to compute the compositional inverses of three classes of the permutation polynomials: (a) the permutation polynomials of the form $ax^q+bx+(x^q-x)^k$ over $\mathbb{F}_{q^2},$ where $a+b \in \mathbb{F}_q^*$ or $a^q=b;$ (b) the permutation polynomials of the forms $f(x)=-x+x^{(q^2+1)/2}+x^{(q^3+q)/2} $ and $f(x)+x$ over $\mathbb{F}_{q^3};$ (c) the permutation polynomial of the form $A^{m}(x)+L(x)$ over $\mathbb{F}_{q^n},$ where ${\rm Im}(A(x))$ is a vector space with dimension $1$ over $\mathbb{F}_{q}$ and $L(x)$ is not a linearized permutation polynomial. |
| title | The compositional inverses of three classes of permutation polynomials over finite fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.11153 |