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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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A note on permutation polynomials over finite fields [PDF]
Finite Fields Their Appl., 2017 Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, two conjectures on permutation polynomials proposed recently by Wu and Li [19] are settled ...
Jingxue Ma, G. Ge
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The Applications of Algebraic Polynomial Rings in Satellite Coding and Cryptography [PDF]
Mathematics Interdisciplinary Research, 2022 This survey illustrates and investigates the application of polynomial rings over finite fields to generate PRN codes for Global Navigation Satellite System (GNSS) satellites.
Amir Bagheri, Hassan Emami
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Using zeta functions to factor polynomials over finite fields [PDF]
Arithmetic Geometry: Computation and
Applications, 2017 In 2005, Kayal suggested that Schoof's algorithm for counting points on elliptic curves over finite fields might yield an approach to factor polynomials over finite fields in deterministic polynomial time.
B. Poonen
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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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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 polynomial factorization over finite fields [PDF]
Mathematics of Computation, 1981 Let f ( x ) f(x)
Gunji, Hiroshi, Arnon, Dennis
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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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On the Planarity of Certain Dembowski-Ostrom Polynomials
Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2022 Planar mappings, defined by Dembowski and Ostrom, are identified as a means to construct projective planes. Then, many important applications of planar mappings appear in different fields such as cryptography and coding theory.
Zehra Aksoy, Barış Bülent Kırlar
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The review on elliptic curves as cryptographic pairing groups [PDF]
Mathematics and Computational Sciences, 2021 Elliptic curve is a set of two variable points on polynomials of degree 3 over a field acted by an addition operation that forms a group structure. The motivation of this study is the mathematics behind that elliptic curve to the applicability within a ...
E Khamseh
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