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

Fuente: arXiv
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Main Authors: Yuan, Pingzhi, Pang, Xuan, Wu, Danyao
Format: Preprint
Published: 2025
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author Yuan, Pingzhi
Pang, Xuan
Wu, Danyao
author_facet Yuan, Pingzhi
Pang, Xuan
Wu, Danyao
contents 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 $\mathbb{F}_{q^2}$.
format Preprint
id arxiv_https___arxiv_org_abs_2503_22415
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Algebraic Structure of Permutational Polynomials over $\mathbb{F}_{q^n}$ \uppercase\expandafter{\romannumeral2}
Yuan, Pingzhi
Pang, Xuan
Wu, Danyao
Number Theory
11T06, 11T55
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 $\mathbb{F}_{q^2}$.
title Algebraic Structure of Permutational Polynomials over $\mathbb{F}_{q^n}$ \uppercase\expandafter{\romannumeral2}
topic Number Theory
11T06, 11T55
url https://arxiv.org/abs/2503.22415