Results 11 to 20 of about 12,890,521 (357)
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) โX over the prime field of a field with characteristic p.
Louis Halle Rowen, Uzi Vishne
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Algebraic Properties of Finite Neutrosophic Fields [PDF]
Neutrosophic Sets and Systems, 2022 We explore a finite Neutrosophic field ๐ญ๐ (๐ฐ) and its Neutrosophic multiplicative group ๐ญ๐ (๐ฐ) ร in this study. We first show |๐ญ๐ (๐ฐ) ร| = (๐ โ ๐) ๐ and then its algebraic properties are studied.
T. Chalapathi +2 more
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Crooked Maps in Finite Fields [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We consider the maps $f:\mathbb{F}_{2^n} โ\mathbb{F}_{2^n}$ with the property that the set $\{ f(x+a)+ f(x): x โF_{2^n}\}$ is a hyperplane or a complement of hyperplane for every $a โ\mathbb{F}_{2^n}^*$.
Gohar Kyureghyan
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FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs [PDF]
Journal of High Energy Physics, 2019 A bstractComplex algebraic calculations can be performed by reconstructing analytic results from numerical evaluations over finite fields. We describe FiniteFlow, a framework for defining and executing numerical algorithms over finite fields and ...
T. Peraro
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Entanglement-assisted quantum error-correcting codes over arbitrary finite fields [PDF]
Quantum Information Processing, 2018 We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well.
C. Galindo +3 more
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Ternary number systems in finite fields [PDF]
ะะพะผะฟัััะตัะฝะฐั ะพะฟัะธะบะฐ, 2018 The work continues the author's previous study of positional number systems in finite fields. The paper considers ternary number systems and arithmetic operations algorithms for the representation of elements of finite fields in the so-called ternary ...
Vladimir Chernov
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On Two-to-One Mappings Over Finite Fields [PDF]
IEEE Transactions on Information Theory, 2019 Two-to-one (2-to-1) mappings over finite fields play an important role in symmetric cryptography. In particular they allow to design APN functions, bent functions and semi-bent functions. In this paper we provide a systematic study of two-to-one mappings
Sihem Mesnager, Longjiang Qu
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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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Minimal Linear Codes over Finite Fields [PDF]
Finite Fields Their Appl., 2018 As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research topic in coding ...
Ziling Heng, C. Ding, Zhengchun Zhou
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Faster Polynomial Multiplication over Finite Fields [PDF]
Journal of the ACM, 2014 Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two polynomials in F_p[X] of degree less than n. For n large compared to p, we establish the bound M_p(n) = O(n log n 8^(log^* n) log p), where log^* is the iterated logarithm ...
David Harvey +2 more
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