Results 1 to 10 of about 2,083 (203)
Probabilistic Galois theory [PDF]
Bulletin of the London Mathematical Society, 2012 We show that there are at most $O_{n, }(H^{n-2+\sqrt{2}+ })$ monic integer polynomials of degree $n$ having height at most $H$ and Galois group different from the full symmetric group $S_n$, improving on the previous 1973 world record $O_{n}(H^{n-1/2}\log H)$.
Rainer Dietmann
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A Novel Cipher-Based Data Encryption with Galois Field Theory [PDF]
Sensors, 2023 Both the act of keeping information secret and the research on how to achieve it are included in the broad category of cryptography. When people refer to “information security,” they are referring to the study and use of methods that make data transfers ...
Mohammad Mazyad Hazzazi +3 more
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Comptes Rendus. MathématiqueLet $L/K$ be a cyclic extension of degree $n = 2m$. It is known that the space $\mathrm{Alt}_K(L)$ of alternating $K$-bilinear forms (skew-forms) on $L$ decomposes into a direct sum of $K$-subspaces $A^{\sigma ^i}$ indexed by the elements of $\mathrm{Gal}
Gupta, Ashish, Mandal, Sugata
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Applications of the Projective Space PG (3,8) in Coding Theory [PDF]
مجلة التربية والعلم, 2023 The main objective of this research is to present the relationship between the subject of coding theory and three-dimensional projection space in the eighth field.
Marwa Almstufa, Nada Yahya
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Two New Classes of Codebooks Asymptotically Achieving the Welch Bound
IEEE Access, 2021 Exponential sums over Galois rings have many applications in coding theory, cryptography and algebraic combinatorics. In this article, we employ additive characters and multiplicative characters over Galois rings to present two classes of codebooks, and ...
Shimin Sun, Li Han, Yang Yan, Yao Yao
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Galois orbits of TQFTs: symmetries and unitarity
Journal of High Energy Physics, 2022 We study Galois actions on 2+1D topological quantum field theories (TQFTs), characterizing their interplay with theory factorization, gauging, the structure of gapped boundaries and dualities, 0-form symmetries, 1-form symmetries, and 2-groups.
Matthew Buican, Rajath Radhakrishnan
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Sur l'existence du sch\'ema en groupes fondametal [PDF]
Épijournal de Géométrie Algébrique, 2020 Let $S$ be a Dedekind scheme, $X$ a connected $S$-scheme locally of finite type and $x\in X(S)$ a section. The aim of the present paper is to establish the existence of the fundamental group scheme of $X$, when $X$ has reduced fibers or when $X$ is ...
Marco Antei +2 more
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Remarks on abstract Galois theory
Manuscrito, 2011 This paper is a historical companion to a previous one, in which it was studied the so-called abstract Galois theory as formulated by the Portuguese mathematician José Sebastião e Silva (see da Costa, Rodrigues (2007)).
Newton C. A. da Costa, Otávio Bueno
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An Efficient Audio Encryption Scheme Based on Finite Fields
IEEE Access, 2021 Finite fields are well-studied algebraic structures with enormous efficient properties which have applications in the fields of cryptology and coding theory.
Dawood Shah +5 more
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Models of abstract and real systems based on broken symmetry group [PDF]
E3S Web of Conferences, 2020 This article shows that symmetry groups as well as broken symmetry groups in natural and abstract mathematical may be used as models of development and evolution objects while describing the states and transformations of such systems.
Gorshkov K.A. +3 more
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