A further study of polynomial $g_{n,q}$ over finite fields
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917551033810944 |
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| author | Fernando, Neranga Kousik, Bhitali |
| author_facet | Fernando, Neranga Kousik, Bhitali |
| contents | Let $n\geq 0$ be an integer and $q$ a prime power. The polynomial $g_{n,q}$ was introduced in [10] with the purpose of finding new classes of permutation polynomials over finite fields. We investigate the permutation behaviour of the polynomial $g_{n,q}(X)$ over finite fields of even characteristic. We introduce the multivariate case of the polynomial $g_{n,q}$, and study the permutation polynomials in several variables and local permutation polynomials resulting from the polynomials $g_{n,q}(X_1,X_2,\ldots , X_k)$. We also present several new identities of $g_{n,q}(X)$, and present some open questions on the permutation property of $g_{n,q}(X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01037 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A further study of polynomial $g_{n,q}$ over finite fields Fernando, Neranga Kousik, Bhitali Number Theory 11T06, 11T55 Let $n\geq 0$ be an integer and $q$ a prime power. The polynomial $g_{n,q}$ was introduced in [10] with the purpose of finding new classes of permutation polynomials over finite fields. We investigate the permutation behaviour of the polynomial $g_{n,q}(X)$ over finite fields of even characteristic. We introduce the multivariate case of the polynomial $g_{n,q}$, and study the permutation polynomials in several variables and local permutation polynomials resulting from the polynomials $g_{n,q}(X_1,X_2,\ldots , X_k)$. We also present several new identities of $g_{n,q}(X)$, and present some open questions on the permutation property of $g_{n,q}(X)$. |
| title | A further study of polynomial $g_{n,q}$ over finite fields |
| topic | Number Theory 11T06, 11T55 |
| url | https://arxiv.org/abs/2606.01037 |