Results 11 to 20 of about 12,115,560 (297)
Dickson polynomials over finite fields [PDF]
Finite Fields and Their Applications, 2012 For any element \(a\) of a finite field \({\mathbb F}_q\) and any integers \(n\geq 1\), \(k\geq 0\), the authors define the \(n\)-th Dickson polynomial of the \((k+1)\)-st kind \(D_{n,k}(x,a)\) over \({\mathbb F}_q\) by \[ D_{n,k}(x,a) =\sum _{i=0}^{n/2} \frac{n-ki}{n-i} \binom{n-i}{i} (-a)^ix^{n-2i}. \] Moreover, for \(n=0\) one puts \(D_{n,k}(x,a) =2-
Qiang Wang 0012, Joseph L. Yucas
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A Class of Polynomials over Finite Fields [PDF]
Finite Fields and Their Applications, 1999 A fundamental and difficult problem in Algebraic Curve Theory over Finite Fields is the computation of the maximal number \(N_q(g)\) of \(\mathbb F_q\)-rational points that a projective, geometrically irreducible, non-singular algebraic curve of genus \(g\) defined over \(\mathbb F_q\) can have. \textit{J.-P.
Garcia, Arnaldo, Stichtenoth, Henning
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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
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Factoring polynomials over arbitrary finite fields [PDF]
Theoretical Computer Science, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tanja Lange 0001, Arne Winterhof
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Specific permutation polynomials over finite fields [PDF]
Finite Fields and Their Applications, 2011 Withdrawn by the author [conflict of copyright]
Marcos, José E.
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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
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Primitive polynomials with prescribed second coefficient [PDF]
, 2006 The Hansen-Mullen Primitivity Conjecture (HMPC) (1992) asserts that, with some (mostly obvious) exceptions, there exists a primitive polynomial of degree n over any finite fieldwith any coefficient arbitrarily prescribed.
Cohen, Stephen D. +3 more
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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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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.
Randell Heyman +3 more
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Random Polynomials Over Finite Fields [PDF]
, 1999 The idea of this thesis is to take some questions about polynomials over finite fields and 'answer' them using probability theory; that is, we give the average behaviour of certain properties of polynomials. We tend to deal with multivariate polynomials,
Sharkey, Andrew
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