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Reconfigurable Galois Field multiplier
2014 International Symposium on Biometrics and Security Technologies (ISBAST), 2014Galois Field has received a lot of attention because of their important and particular applications in cryptography, channel coding, etc. This paper presents the Reconfigurable Galois Field multiplier used to calculate the Galois field multiplication of different lengths which consists of AND gates and special cells.
Rong-Jian Chen
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Galois extensions and $$O^{*}$$-fields
Positivity, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kenneth Evans, Jingjing Ma
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On the Galois Theory of Differential Fields
American Journal of Mathematics, 19551. Summary. In a preceding paper [7] there was presented a Galois theory, for a certaini kind of differenitial field extension called strongly normal. The Galois group of a strongly normal extension is enidowed with a structure very much like that of a group variety, as studied by Weil [14].
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Galois theory for fuzzy fields
Fuzzy Sets and Systems, 2001Let \(F/K\) be a field extension and let \(G(F/K)\) denote the Galois group of \(F/K\). In this paper the author develops a generalized form of the Galois connection between the intermediate fields of a field extension and the subgroups of \(G(F/K)\). In particular, the author extends the Galois connection to include fuzzy intermediate fields of \(F/K\)
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On the geometry of galois cubic fields
Mathematical Notes, 2011The paper under review is concerned with studying the Galois fields over \(\mathbb{Q}\) of polynomials of the type \(f(x) = x^3 - kx +k\), where \(k\) is a positive integer, where \(f\) is irreducible over \(\mathbb{Q}\), and where the discriminant of \(f\) is a complete square.
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Geometry and dynamics of Galois fields
Russian Mathematical Surveys, 2004Summary: The tables defining operations in finite fields possess many properties of tables of random numbers. A distinctive variant is discussed of automorphisms of tori in the theory of dynamical systems for which a torus has finitely many points. Also established are the actions of Frobenius transformations of finite fields onto projective structures
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Field Theory of Galois' Fields
1995The motivation for the present work comes from various sources which, however, need not be elaborated on here. I will be exploring a class of quantum field theories defined over finite sets of integers. Essentially these are the familiar Z„ lattice theories, but carried to their logical extremes.
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2015
A small portion of linear algebra and combinatorics are used in the development of Hamming codes, the first generation error control codes. The design of error control codes such as BCH codes and Reed Solomon codes relies on the structures of Galois fields and polynomials over Galois fields.
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A small portion of linear algebra and combinatorics are used in the development of Hamming codes, the first generation error control codes. The design of error control codes such as BCH codes and Reed Solomon codes relies on the structures of Galois fields and polynomials over Galois fields.
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1984
If F is an algebraic number field of degree n over Q and p is a prime, then F is p-realizable if there is a tor-sionfree abelian group A of rank n such that qA = A for all prines q i p and F is isomorphic to the quasi-endomorphism algebra of A. The question “for which F and p is F p-realizable?” was the subject of the paper by Pierce and Vinsonhaler ...
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If F is an algebraic number field of degree n over Q and p is a prime, then F is p-realizable if there is a tor-sionfree abelian group A of rank n such that qA = A for all prines q i p and F is isomorphic to the quasi-endomorphism algebra of A. The question “for which F and p is F p-realizable?” was the subject of the paper by Pierce and Vinsonhaler ...
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