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arXiv · 2503.22415

Algebraic Structure of Permutational Polynomials over $\mathbb{F}_{q^n}$ \uppercase\expandafter{\romannumeral2}

Pingzhi Yuan·Xuan Pang·Danyao Wu
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Abstract

It is well known that there exists a significant equivalence between the vector space $\mathbb{F}_{q}^n$ and the finite fields $\mathbb{F}_{q^n}$, and many scholars often view them as the same in most contexts. However, the precise connections between them still remain mysterious. In this paper, we first show their connections from an algebraic perspective, and then propose a more general algebraic framework theorem. Furthermore, as an application of this generalized algebraic structure, we give some classes of permutation polynomials over $\mathbb{F}_{q^2}$.

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Pingzhi Yuan, Xuan Pang, Danyao Wu. 2025-03-28. Algebraic Structure of Permutational Polynomials over $\mathbb{F}_{q^n}$ \uppercase\expandafter{\romannumeral2}. https://arxiv.org/abs/2503.22415

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