Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSome results about permutation properties of a kind of binomials over finite fields
71
0
0.0
(
0
)
Added by
Xiaogang Liu
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Authors
Xiaogang Liu
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 studies, and get some further results about the permutation properties of the permutation polynomials. Also, some new classes of permutation polynomials are constructed. For these, we alter the coefficients, exponents or the underlying fields, etc.
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 interleavers. Furthermore we employ Skolem sequences in order to find new interleavers with known cycle structure. In the case of Redei functions an exact formula for the inverse function is derived. The cycle structure of Redei functions is also investigated. The self-inverse and non-self-inver
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 it is shown that the presented results are the generalizations of some earlier works.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
