Related papers: Four new classes of permutation trinomials and the…

In this paper we use algebraic curves and other algebraic number theory methods to show the validity of a permutation polynomial conjecture regarding $f(X)=X^{q(p-1)+1} +\alpha X^{pq}+X^{q+p-1}$, on finite fields $\mathbb{F}_{q^2}, q=p^k$,…

We construct classes of permutation polynomials over F_{Q^2} by exhibiting classes of low-degree rational functions over F_{Q^2} which induce bijections on the set of (Q+1)-th roots of unity in F_{Q^2}. As a consequence, we prove two…

We study compositional inverses of permutation polynomials, complete mappings, mutually orthogonal Latin squares, and bent vectorial functions. Recently it was obtained in [33] the compositional inverses of linearized permutation binomials…

For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…

We classify complete permutation polynomials of type $aX^{\frac{q^n-1}{q-1}+1}$ over the finite field with $q^n$ elements, for $n+1$ a prime and $n^4 < q$. For the case $n+1$ a power of the characteristic we study some known families. We…

In this paper, a construction of complete permutation polynomials over finite fields of even characteristic proposed by Tu et al. recently is generalized in a recursive manner. Besides, several classes of complete permutation polynomials…

Let $p$ be an odd prime and $e$ be a positive integer. We completely explain the permutation binomials and trinomials arising from the reversed Dickson polynomials of the $(k+1)$-th kind $D_{n,k}(1,x)$ over $\mathbb{F}_{p^e}$ when…

Motivated by recent results on the constructions of permutation polynomials with few terms over the finite field $\mathbb{F}_{2^n}$, where $n$ is a positive even integer, we focus on the construction of permutation trinomials over…

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…

In this paper, we investigate permutation polynomials over the finite field $\mathbb F_{q^n}$ with $q=2^m$, focusing on those in the form $\mathrm{Tr}(Ax^{q+1})+L(x)$, where $A\in\mathbb F_{q^n}^*$ and $L$ is a $2$-linear polynomial over…

In this work, we completely characterize (i) permutation binomials of the form $x^{{{2^n -1}\over {2^t-1}}+1}+ ax \in \mathbb{F}_{2^n}[x], n = 2^st, a \in \mathbb{F}_{2^{2t}}^{*}$, and (ii) permutation trinomials of the form…

We study the compositional inverses of some general classes of permutation polynomials over finite fields. We show that we can write these inverses in terms of the inverses of two other polynomials bijecting subspaces of the finite field,…

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…

Recently, Tu, Zeng, Li, and Helleseth considered trinomials of the form $f(X)=X+aX^{q(q-1)+1}+bX^{2(q-1)+1}\in\Bbb F_{q^2}[X]$, where $q$ is even and $a,b\in\Bbb F_{q^2}^*$. They found sufficient conditions on $a,b$ for $f$ to be a…

Let $q>2$ be a prime power and $f={\tt x}^{q-2}+t{\tt x}^{q^2-q-1}$, where $t\in\Bbb F_q^*$. It was recently conjectured that $f$ is a permutation polynomial of $\Bbb F_{q^2}$ if and only if one of the following holds: (i) $t=1$, $q\equiv…

In this paper, we present the compositional inverses of several classes permutation polynomials of the form $\sum_{i=1}^kb_i\left({\rm Tr}_m^{mn}(x)^{t_i}+\delta\right)^{s_i}+f_1(x)$, where $1\leq i \leq k,$ $s_i$ are positive integers,…

In this paper, we propose a new method to obtain new permutation polynomials over $\mathbb{F}_{q^2}$. Using this method, we extend many known permutation polynomials, which take the form $\sum_i(x^q-x+\delta)^{s_i}+L(x)$, where $L(x)$ is a…

Permutation polynomials with few terms attracts researchers' interest in recent years due to their simple algebraic form and some additional extraordinary properties. In this paper, by analyzing the quadratic factors of a fifth-degree…

We present several existence and nonexistence results for permutation binomials of the form $x^r(x^{q-1}+a)$, where $e\geq 2$ and $a\in \mathbb{F}_{q^e}^*$. As a consequence, we obtain a complete characterization of such permutation…

We determine all permutation trinomials of type $x^{2p^s+r}+x^{p^s+r}+\lambda x^r$ over the finite field $\mathbb{F}_{p^t}$ when $(2p^s+r)^4<p^t$. This partially extends a previous result by Bhattacharya and Sarkar in the case $p=2$, $r=1$.