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Visibly irreducible polynomials over finite fields [PDF]
The American Mathematical Monthly, 2018 H. Lenstra has pointed out that a cubic polynomial of the form (x-a)(x-b)(x-c) + r(x-d)(x-e), where {a,b,c,d,e} is some permutation of {0,1,2,3,4}, is irreducible modulo 5 because every possible linear factor divides one summand but not the other.
O'Dorney, Evan M.
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Primitive Polynomials Over Finite Fields [PDF]
Mathematics of Computation, 1992 In this note we extend the range of previously published tables of primitive polynomials over finite fields. For each p n > 10 50 {p^n} > {10^{50}} with p ≤ 97
Hansen, Tom, Mullen, Gary L.
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Uniform estimates for smooth polynomials over finite fields
Discrete Analysis, 2023 Uniform estimates for smooth polynomials over finite fields, Discrete Analysis 2023:16, 31 pp. A positive integer $n$ is called $m$-_smooth_ if its largest prime factor has size at most $m$.
Ofir Gorodetsky
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On Some Computational and Applications of Finite Fields
Ratio Mathematica, 2020 Finite field is a wide topic in mathematics. Consequently, none can talk about the whole contents of finite fields. That is why this research focuses on small content of finite fields such as polynomials computational, ring of integers modulo p where p ...
Jean Pierre Muhirwa
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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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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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r-fat linearized polynomials over finite fields [PDF]
Journal of Combinatorial Theory, Series A, 2022 In this paper we prove that the property of being scattered for a $\mathbb{F}_q$-linearized polynomial of small $q$-degree over a finite field $\mathbb{F}_{q^n}$ is unstable, in the sense that, whenever the corresponding linear set has at least one point of weight larger than one, the polynomial is far from being scattered.
D. Bartoli +3 more
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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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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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A Robust Version of Heged\H{u}s's Lemma, with Applications [PDF]
TheoretiCS, 2023 Heged\H{u}s's lemma is the following combinatorial statement regarding polynomials over finite fields. Over a field $\mathbb{F}$ of characteristic $p > 0$ and for $q$ a power of $p$, the lemma says that any multilinear polynomial $P\in \mathbb{F}[x_1 ...
Srikanth Srinivasan
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