Orthomorphism Polynomials of degree $7$ over finite fields
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917229399900160 |
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| author | Kousik, Bhitali Basnet, Dhiren Kumar |
| author_facet | Kousik, Bhitali Basnet, Dhiren Kumar |
| contents | In 2019, Xiang Fan \cite{xfan} classified all permutation polynomials of degree $7$ over finite fields of odd characteristics. In this paper, we use this classification to determine the complete list of degree $7$ orthomorphism polynomials over finite fields of order $q\in\{11,~13,~17,~19,~25,~49\}.$ In addition, the non-existence of these polynomials is established for certain fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orthomorphism Polynomials of degree $7$ over finite fields Kousik, Bhitali Basnet, Dhiren Kumar Number Theory 11T06, 11T55, 12Y05 In 2019, Xiang Fan \cite{xfan} classified all permutation polynomials of degree $7$ over finite fields of odd characteristics. In this paper, we use this classification to determine the complete list of degree $7$ orthomorphism polynomials over finite fields of order $q\in\{11,~13,~17,~19,~25,~49\}.$ In addition, the non-existence of these polynomials is established for certain fields. |
| title | Orthomorphism Polynomials of degree $7$ over finite fields |
| topic | Number Theory 11T06, 11T55, 12Y05 |
| url | https://arxiv.org/abs/2507.10316 |