Results 131 to 140 of about 503 (178)
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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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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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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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Large Fields in Differential Galois Theory
Journal of the Institute of Mathematics of Jussieu, 2021Annette Bachmayr +2 more
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Some Advantages of Non-Binary Galois Fields for Digital Signal Processing
Indonesian Journal of Electrical Engineering and Computer Science, 2021Dina B Shaltykova +2 more
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