Results 11 to 20 of about 12,820,749 (293)

Some properties of generalized self-reciprocal polynomials over finite fields [PDF]

Romanian Journal of Mathematics and Computer Science, 2014
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4].
Ryul Kim, Ok-Hyon Song, Hyon-Chol Ri
doaj   +2 more sources

On evaluating multivariate polynomials over finite fields

Quaestiones Mathematicae, 2015
Some evaluation methods of multivariate polynomials over finite fields are described and their multiplicative complexity is discussed.Keywords: Multiplicative complexity, complexity, multivariate polynomials, finite fields, computational ...
Ballico, Edoardo, Elia, M.
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Symmetric polynomials over finite fields

Finite Fields and Their Applications, 2023
v2: minor ...
Mátyás Domokos, Botond Miklósi
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Permutation Polynomials over Finite Fields and their application to Cryptography [PDF]

, 2023
The aim of the paper is the study of Permutation Polynomials over finite fields and their application to cryptography. In this paper, I will begin by a brief review of finite fields, define permutation polynomials over finite fields and their properties.
Benseba, Katia
core   +1 more source

On the number of factorizations of polynomials over finite fields [PDF]

Journal of Combinatorial Theory, Series A, 2020
Motivated by coding applications,two enumeration problems are considered: the number of distinct divisors of a degree-m polynomial over F = GF(q), and the number of ways a polynomial can be written as a product of two polynomials of degree at most n over F.
Rachel N. Berman, Ron M. Roth
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Degree of orthomorphism polynomials over finite fields [PDF]

Finite Fields and Their Applications, 2021
An orthomorphism over a finite field $\mathbb{F}_q$ is a permutation $θ:\mathbb{F}_q\mapsto\mathbb{F}_q$ such that the map $x\mapstoθ(x)-x$ is also a permutation of $\mathbb{F}_q$. The degree of an orthomorphism of $\mathbb{F}_q$, that is, the degree of the associated reduced permutation polynomial, is known to be at most $q-3$. We show that this upper
Jack Allsop, Ian M. Wanless
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The additive index of polynomials over finite fields [PDF]

Finite Fields and Their Applications, 2022
In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms of their additive indices, such as value set sizes, bounds on multiplicative character sums, and characterizations of permutation polynomials.
Lucas Reis, Qiang Wang 0012
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On Values of Cyclotomic Polynomials. V [PDF]

, 2003
In this paper, we present three results on cyclotomic polynomials. First, we present results about factorization of cyclotomic polynomials over arbitrary fields K.
Motose, Kaoru, Kaoru Motose
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Palindromic Polynomials over Finite Fields

, 2022
For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application is given for systems of linear equations over $\mathbb{F}$ of index $2$.
Price, Geoffrey L., Thompson, Katherine
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On polynomial factorization over finite fields [PDF]

Mathematics of Computation, 1981
Let f ( x ) f(x)
Gunji, Hiroshi, Arnon, Dennis
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