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arXiv · 2507.10316

Orthomorphism Polynomials of degree $7$ over finite fields

Bhitali Kousik·Dhiren Kumar Basnet
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Abstract

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.

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Bhitali Kousik, Dhiren Kumar Basnet. 2025-07-14. Orthomorphism Polynomials of degree $7$ over finite fields. https://arxiv.org/abs/2507.10316

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