Results 31 to 40 of about 127,631 (176)
Tuples of polynomials over finite fields with pairwise coprimality conditions [PDF]
, 2018 Let q be a prime power. We estimate the number of tuples of degree bounded monic polynomials (Q1, . . . , Qv) ∈ (Fq[z])v that satisfy given pairwise coprimality conditions.
Arias de Reyna Martínez, Juan +1 more
core +1 more source
Primitive Normal Polynomials Over Finite Fields [PDF]
Mathematics of Computation, 1994 Summary: We significantly extend the range of published tables of primitive normal polynomials over finite fields. For each \(p^ n < 10^{50}\) with \(p \leq 97\), we provide a primitive normal polynomial of degree \(n\) over \(\mathbb{F}_ p\).
Morgan, Ilene H., Mullen, Gary L.
openaire +1 more source
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
core +1 more source
Classes of weak Dembowski–Ostrom polynomials for multivariate quadratic cryptosystems
Journal of Mathematical Cryptology, 2015 T. Harayama and D. K. Friesen [J. Math. Cryptol. 1 (2007), 79–104] proposed the linearized binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski–Ostrom (DO) polynomials in this framework over the finite field 𝔽2.
Alam Bilal, Özbudak Ferruh, Yayla Oğuz
doaj +1 more source
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
Efficient Algorithm for Finding Roots of Error-Locator Polynomials
IEEE Access, 2021 A novel method for finding roots of polynomials over finite fields has been proposed. This method is based on the cyclotomic discrete Fourier transform algorithm. The improvement is achieved by using the normalized cyclic convolutions, which have a small
Sergei Valentinovich Fedorenko
doaj +1 more source
Characterization and Enumeration of Good Punctured Polynomials over Finite Fields
International Journal of Mathematics and Mathematical Sciences, 2016 A family of good punctured polynomials is introduced. The complete characterization and enumeration of such polynomials are given over the binary field F2.
Somphong Jitman +4 more
doaj +1 more source
Linearized polynomials over finite fields revisited
, 2013 We give new characterizations of the algebra $\mathscr{L}_n(\mathbb{F}_{q^n})$ formed by all linearized polynomials over the finite field $\mathbb{F}_{q^n}$ after briefly surveying some known ones.
Liu, Zhuojun, Wu, Baofeng
core +1 more source
Factoring Polynomials over Special Finite Fields
Finite Fields and Their Applications, 2001 The main result of this paper is a theoretical algorithm to factorize polynomials over large finite fields (Theorem~1 below). Let \(\Phi_k\) be the \(k\)th cyclotomic polynomial. Then the authors prove the following results. Theorem 1. There is a deterministic algorithm such that, for some constant \(c>0\) -- given a prime \(p\), positive integers \(n\)
Lenstra, H.W. +2 more
openaire +3 more sources
Constructing irreducible polynomials with prescribed level curves over finite fields
International Journal of Mathematics and Mathematical Sciences, 2001 We use Eisenstein's irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X,Y)∈GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc:={(x,y)∈GF(q)2|P(x,y)=c}.
Mihai Caragiu
doaj +1 more source