Some new classes of permutation polynomials and their compositional inverses

[2407.12688] Some new classes of permutation polynomials and their compositional inverses Skip to main content Search Submit Donate Log in Mathematics > Number Theory arXiv:2407.12688 (math) [Submitted on 17 Jul 2024] Title: Some new classes of permutation polynomials and their compositional inverses Authors: Sartaj Ul Hasan , Ramandeep Kaur View PDF HTML (experimental) Abstract: We focus on the permutation polynomials of the form $L(X)+\Tr_{m}^{3m}(X)^{s}$ over $\F_{q^3}$, where $\F_q$ is the finite field with $q=p^m$ elements, $p$ is a prime number, $m$ is a positive integer, $\Tr_{m}^{3m}$ is the relative trace function from $\F_{p^{3m}}$ to $\F_{p^{m}}$, $L(X)$ is a linearized polynomial over $\F_{q^{3}}$, and $s>1$ is a positive integer. More precisely, we present six new classes of permutation polynomials over $\F_{q^3}$ of the aforementioned form: one class over finite fields of even characteristic, three classes over finite fields of odd characteristic, and the remaining two over finite fields of arbitrary characteristic. Furthermore, we show that these classes of permutation polynomials are inequivalent to the known ones of the same form. We also provide the explicit expressions for the compositional inverses of each of these classes of permutation polynomials. Comments: 17 pages Subjects: Number Theory (math.NT) Cite as: arXiv:2407.12688 [math.NT] (or arXiv:2407.12688v1 [math.NT] for this version) https://doi.org/10.48550/arXiv.2407.12688 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Finite Fields and Their Applications, Vol. 108, Article No. 102685, 2025 Related DOI : https://doi.org/10.1016/j.ffa.2025.102685 Focus to learn more DOI(s) linking to related resources Submission history From: Sartaj Ul Hasan [ view email ] [v1] Wed, 17 Jul 2024 16:09:12 UTC (18 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2024-07 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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