ﻻ يوجد ملخص باللغة العربية
Permutation polynomials have many applications in finite fields theory, coding theory, cryptography, combinatorial design, communication theory, and so on. Permutation binomials of the form $x^{r}(x^{q-1}+a)$ over $mathbb{F}_{q^2}$ have been studied before, K. Li, L. Qu and X. Chen proved that they are permutation polynomials if and only if $r=1$ and $a^{q+1} ot=1$. In this paper, we consider the same binomial, but over finite fields $mathbb{F}_{q^3}$ and $mathbb{F}_{q^e}$. Two different kinds of methods are employed, and some partial results are obtained for them.
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 their stud
For the finite field $mathbb{F}_{2^{3m}}$, permutation polynomials of the form $(x^{2^m}+x+delta)^{s}+cx$ are studied. Necessary and sufficient conditions are given for the polynomials to be permutation polynomials. For this, the structures and properties of the field elements are analyzed.
In this work we establish some new interleavers based on permutation functions. The inverses of these interleavers are known over a finite field $mathbb{F}_q$. For the first time M{o}bius and Redei functions are used to give new deterministic interle
In this paper, we show that LCD codes are not equivalent to linear codes over small finite fields. The enumeration of binary optimal LCD codes is obtained. We also get the exact value of LD$(n,2)$ over $mathbb{F}_3$ and $mathbb{F}_4$. We study the bound of LCD codes over $mathbb{F}_q$.
In this paper, a class of permutation trinomials of Niho type over finite fields with even characteristic is further investigated. New permutation trinomials from Niho exponents are obtained from linear fractional polynomials over finite fields, and