Results 71 to 80 of about 98,739 (338)
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
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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
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Visibly Irreducible Polynomials over Finite Fields [PDF]
The American Mathematical Monthly, 2020 11 pages.
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Hulls of cyclic and negacyclic codes over finite fields [PDF]
, 2014 We study the hulls of cyclic and negacyclic codes of length n over a finite field Fq with respect to the Euclidean and Hermitian inner products. Based on the characterization of their generator polynomials, the dimensions of the hulls of cyclic and ...
Sangwisut, Ekkasit +3 more
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Permutation polynomials of degree 8 over finite fields of characteristic 2 [PDF]
Finite Fields Their Appl., 2019 Up to linear transformations, we obtain a classification of permutation polynomials (PPs) of degree 8 over F 2 r with r > 3 . By Bartoli et al. (2017) [1] , a polynomial f of degree 8 over F 2 r is exceptional if and only if f − f ( 0 ) is a linearized ...
Xiang Fan
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Periodic Points of Polynomials over Finite Fields [PDF]
, 2022 Fix an odd prime p. If r is a positive integer and f is a polynomial with coefficients in Fpr, let Pp,r(f) be the proportion of P1(Fpr) that is periodic with respect to f.
Garton, Derek
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Dickson Polynomials and Irreducible Polynomials Over Finite Fields
Journal of Number Theory, 1994 For the finite field of order \(q\), \(\mathbb{F}_ q\), let \[ D_ n(x,a)= \sum_{j=0}^{\lfloor n/2\rfloor} {\textstyle {n \over {n-j}}} \left( \begin{smallmatrix} n-j\\ j\end{smallmatrix} \right) (-a)^ j x^{n-2j} \] denote the Dickson polynomial of degree \(n\) with parameter \(a\in \mathbb{F}_ q\).
Gao, S.H., Mullen, G.L.
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A new algorithm for factoring polynomials over finite fields [PDF]
, 1981 We present a new probabilistic algorithm for factoring polynomials over finite fields.
D. Cantor, H. Zassenhaus
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Advanced Functional Materials, EarlyView.Two‐photon grayscale lithography (2GL) enables high‐speed and precise 3D printing of thermolyzed silica glass microstructures with optical‐grade surface quality, high quality factors, and mechanical strength utilizing a custom‐made pre‐glass resist based on polyhedral oligomeric silsesquioxane (POSS) modified with a high‐sensitivity Norrish type II ...
Jonathan L. G. Schneider +4 more
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Fixed Points of the Dickson Polynomials of the Second Kind
Journal of Applied Mathematics, 2013 The permutation behavior of Dickson polynomials of the first kind has been extensively studied, while such behavior for Dickson polynomials of the second kind is less known.
Adama Diene, Mohamed A. Salim
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