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Permutation rational functions over finite fields have attracted much attention in recent years. In this paper, we introduce a class of permutation rational functions over $\mathbb F_{q^2}$, whose numerators are so-called $q$-quadratic…

Number Theory · Mathematics 2024-01-25 Ruikai Chen , Sihem Mesnager

This paper considers permutation polynomials over the finite field $F_{q^2}$ in even characteristic by utilizing low-degree permutation rational functions over $F_q$. As a result, we obtain two classes of permutation binomials and six…

Cryptography and Security · Computer Science 2025-08-25 Kirpa Garg , Sartaj Ul Hasan , Chunlei Li , Hridesh Kumar , Mohit Pal

Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many…

Number Theory · Mathematics 2025-02-27 Xuan Pang , Pingzhi Yuan , Hongjian Li

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…

Information Theory · Computer Science 2013-08-28 Pingzhi Yuan , Cunsheng Ding

We determine all permutations in two large classes of polynomials over finite fields, where the construction of the polynomials in each class involves the denominators of a class of rational functions generalizing the classical Redei…

Number Theory · Mathematics 2023-05-11 Zhiguo Ding , Michael E. Zieve

In this paper, we present a linear algebraic approach to the study of permutation polynomials that arise from linear maps over a finite field $\mathbb{F}_{q^2}$. We study a particular class of permutation polynomials over…

Combinatorics · Mathematics 2022-12-09 Megha M. Kolhekar , Harish K. Pillai

We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first charac- terize some functions having linear translators, based on which several families of…

Information Theory · Computer Science 2016-12-13 Nastja Cepak , Pascale Charpin , Enes Pasalic

Permutation polynomials over finite fields have taken an important role in vast areas in mathematics as well as engineering. Recently, Tu et al. gave some classes of complete permutation polynomials over finite fields of even…

Number Theory · Mathematics 2014-04-14 Kitae Kim , Ikkwon Yie

Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication…

Information Theory · Computer Science 2015-09-01 Kangquan Li , Longjiang Qu , Xi Chen

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…

Number Theory · Mathematics 2013-12-20 Baofeng Wu , Dongdai Lin

We present a few factorizations of polynomials over finite fields. These factorizations are related to traces, compositions of polynomials and binomial coefficients. As a corollary we obtain a description of all irreducible polynomials…

Number Theory · Mathematics 2007-05-23 Roland Bacher

Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, two conjectures on permutation polynomials proposed recently by Wu and Li [19] are…

Combinatorics · Mathematics 2017-03-10 Jingxue Ma , Gennian Ge

Let ${\mathbb F}_q$ be a finite field of characteristic two and ${\mathbb F}_q(X_1,...,X_n)$ a rational function field. We use matrix methods to obtain explicit transcendental bases of the invariant subfields of orthogonal groups and…

Commutative Algebra · Mathematics 2007-05-23 Zhongming Tang , Zhe-xian Wan

In this paper, we make use of the classification results of low-degree permutation rational functions together with their geometric properties to investigate rational functions that induce permutations on the multiplicative subgroup mu_q+1,…

Number Theory · Mathematics 2026-05-13 Yi Li , Deng Tang

Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature…

Information Theory · Computer Science 2014-02-25 Cunsheng Ding , Longjiang Qu , Qiang Wang , Jin Yuan , Pingzhi Yuan

Let $\mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with…

Information Theory · Computer Science 2019-07-09 Xiaogang Liu

The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.

Number Theory · Mathematics 2010-08-12 Melsik K. Kyuregyan , Gohar M. Kyureghyan

Permutation trinomials over finite fields consititute an active research due to their simple algebraic form, additional extraordinary properties and their wide applications in many areas of science and engineering. In the present paper, six…

Information Theory · Computer Science 2016-05-23 Kangquan Li , Longjiang Qu , Chao Li , Shaojing Fu

For a subgroup of $PGL(2,q)$ we show how some irreducible polynomials over $\mathbb{F}_q$ arise from the field of invariant rational functions. The proofs rely on two actions of $PGL(2,F)$, one on the projective line over a field $F$ and…

Number Theory · Mathematics 2021-08-27 Rod Gow , Gary McGuire

Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, four classes of monomial complete permutation polynomials and one class of…

Information Theory · Computer Science 2016-06-15 Jingxue Ma , Tao Zhang , Tao Feng , Gennian Ge
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