Hermitian Dickson Dualities for Codes over Near-Fields
MathematicsA Dickson near-field is obtained from Fp2 by twisting multiplication so that distributivity holds only on the right. In this work, we develop a basic theory of right-linear codes of length n over NF(p2).
Altaf Alshuhail, Fozaiyah A. Al-hubairah
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Congruences of Galois representations attached to effective A-motives over global function fields [PDF]
International Journal of Number Theory, 2022 This article investigates congruences of $\mathfrak{p}$-adic representations arising from effective $A$-motives defined over a global function field $K$.
Y. Okumura
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Galois groups of uplifted de Sitter vacua [PDF]
Annals of Physics, 2023 We compute the Galois group of a polynomial whose roots are determined by the critical points of a scalar potential in type IIB compactifications. We focus our study on certain perturbative models where it is feasible to construct a de Sitter vacuum ...
C. Damian, O. Loaiza-Brito
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An effective open image theorem for products of principally polarized abelian varieties [PDF]
Journal of Number Theory, 2022 Let $A = \prod_{1\leq i\leq n} A_i$ be the product of principally polarized abelian varieties $A_1, \ldots, A_n$ of dimensions $g_1, \ldots, g_n$, respectively, each defined over a number field $K$, and pairwise nonisogenous over $\overline{K}$.
Jacob Mayle, Tianxin Wang
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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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Generation modulo the action of a permutation group [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the generation of unlabeled graph up to an isomorphism.
Nicolas Borie
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The algorithm for encryption of graphic information based on chaotic map and galois field transform
Informatics and Mathematical Methods in Simulation, 2023 The current stage of development of information technologies is characterized by a significant increase in the use of graphic data, i.e., digital video and digital images combined with the widespread use of resource-constrained platforms, such as IoT and
O. Palagin, A.V. Sokolov
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Galois symmetry induced by Hecke relations in rational conformal field theory and associated modular tensor categories [PDF]
Journal of Physics A: Mathematical and Theoretical, 2019 Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras.
J. Harvey, Yichen Hu, Yuxiao Wu
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Constructive Galois Connections [PDF]
Journal of functional programming, 2018 Galois connections are a foundational tool for structuring abstraction in semantics, and their use lies at the heart of the theory of abstract interpretation.
David Darais, David Van Horn
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Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence [PDF]
Mathematische Annalen, 2015 The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations, via the parameterized and differential Galois theories.
C. Hardouin +2 more
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