Results 41 to 50 of about 53,079 (211)
Quantum Information: A Brief Overview and Some Mathematical Aspects
Mathematics, 2018 The aim of the present paper is twofold. First, to give the main ideas behind quantum computing and quantum information, a field based on quantum-mechanical phenomena. Therefore, a short review is devoted to (i) quantum bits or qubits (and more generally
Maurice R. Kibler
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, 2001 Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups.
Francis Borceux, George Janelidze
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LOCAL EXTENSIONS WITH IMPERFECT RESIDUE FIELD
Ural Mathematical Journal, 2019 The paper deals with some aspects of general local fields and tries to elucidate some obscure facts. Indeed, several questions remain open, in this domain of research, and literature is getting scarce.
Akram Lbekkouri
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The automorphisms and error orbits of Reed – Solomon codes
Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki, 2020 The purpose of this work with its results presented in the article was to develop and transfer to the class of Reed – Solomon codes (RS-codes) the basic provisions of the theory of syndrome norms (TNS), previously developed for the noise-resistant coding
S. I. Semyonov, V. A. Lipnitsky
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GRUPOS DE PERMUTAÇÕES E GRUPOS FINITOS SIMPLES
Colloquium Exactarum, 2011 The normality of subgroups in a finite group has a property discovered by E. Galois in 1832, study-group of permutations of roots of polynomial equations.
Lauro Maycon Fernandes Ferreira +2 more
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On Contradiction and Inclusion Using Functional Degrees
International Journal of Computational Intelligence Systems, 2020 The notion of inclusion is a cornerstone in set theory and therefore, its generalization in fuzzy set theory is of great interest. The degree of f-inclusion is one generalization of such a notion that differs from others existing in the literature ...
Nicolás Madrid, Manuel Ojeda-Aciego
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Khronos, 2016 This paper stresses a specific line of development of the notion of finite field, from Évariste Galois’s 1830 “Note sur la théorie des nombres,” and Camille Jordan’s 1870 Traité des substitutions et des équations algébriques, to Leonard Dickson’s 1901 ...
Frédéric BRECHENMACHER
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PROPERTIES OF GROUPS G OF DOUBLE ERRORS AND ITS INVARIANTS IN BCH CODES
Системный анализ и прикладная информатика, 2018 The goal of the work is the further extending the scope of application of code automorthism in methods and algorithms of error correction by these codes. The effectiveness of such approach was demonstrated by norm of syndrome theory that was developed by
V. A. Lipnitskij, A. V. Serada
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PRIMITIVE MATRICES AND GENERATORS OF PSEUDO RANDOM SEQUENCES OF GALOIS
Ìнформаційні технології в освіті, 2014 In theory and practice of information cryptographic protection one of the key problems is the forming a binary pseudo-random sequences (PRS) with a maximum length with acceptable statistical characteristics.
A. Beletsky, E. Beletsky
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On local Galois deformation rings: generalised tori
Forum of Mathematics, SigmaWe study deformation theory of mod p Galois representations of p-adic fields with values in generalised tori, such as L-groups of (possibly non-split) tori.
Vytautas Paškūnas, Julian Quast
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