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Formalized MathematicsSummary We continue the formalization of field theory in Mizar. Here we prove existence and uniqueness of finite fields by constructing the splitting field of the polynomial X(pn) βX over the prime field of a field with characteristic p.
Louis Halle Rowen, Uzi Vishne
semanticscholar +6 more sources
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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Discrete logarithm problem in matrix
Lietuvos Matematikos Rinkinys, 2023 In this paper the discrete logarithm problem in matrix in finite fields is formulated, possible ways of solution are given.
Povilas Tvarijonas +2 more
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Crooked Maps in Finite Fields [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We consider the maps $f:\mathbb{F}_{2^n} β\mathbb{F}_{2^n}$ with the property that the set $\{ f(x+a)+ f(x): x βF_{2^n}\}$ is a hyperplane or a complement of hyperplane for every $a β\mathbb{F}_{2^n}^*$.
Gohar Kyureghyan
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Permutations involving squares in finite fields
Electronic Research Archive, 2022 Let $ p $ be an odd prime and let $ \mathbb{F}_p $ be the finite field of $ p $ elements. In 2019, Sun studied some permutations involving squares in $ \mathbb{F}_p $. In this paper, by the theory of local fields we generalize this topic to $ \mathbb{F}_{
Hai-Liang Wu, Li-Yuan Wang
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Algebraic Properties of Finite Neutrosophic Fields [PDF]
Neutrosophic Sets and Systems, 2022 We explore a finite Neutrosophic field ππ (π°) and its Neutrosophic multiplicative group ππ (π°) Γ in this study. We first show |ππ (π°) Γ| = (π β π) π and then its algebraic properties are studied.
T. Chalapathi +2 more
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Proper toric maps over finite fields [PDF]
, 2015 We determine a strong form of the decomposition theorem for proper toric maps over finite fields.Comment: to appear in IMRN; change from v1: Lemma 2.4.1 corrected; no effect on the rest of the ...
De Cataldo, M.
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Parallel machine arithmetic for recurrent number systems in non-quadratic fields [PDF]
ΠΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½Π°Ρ ΠΎΠΏΡΠΈΠΊΠ°, 2020 The paper proposes a new method of synthesis of computer arithmetic systems for "error-free" parallel calculations. The difference between the proposed approach and calculations in traditional systems of Residue Number Systems for the direct sum of ...
Vladimir Chernov
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Chebyshev Action on Finite Fields [PDF]
, 2013 Given a polynomial f and a finite field F one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under f.
Gassert, T. Alden
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A Note on Powers in Finite Fields [PDF]
, 2015 The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research.
Aabrandt, Andreas +1 more
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