Results 61 to 70 of about 53,379 (231)

A history of Galois fields

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
doaj  

Periodic points of rational functions over finite fields

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract For q$q$ a prime power and ϕ$\phi$ a rational function with coefficients in Fq$\mathbb {F}_q$, let p(q,ϕ)$p(q,\phi)$ be the proportion of P1Fq$\mathbb {P}^1\left(\mathbb {F}_q\right)$ that is periodic with respect to ϕ$\phi$. Furthermore, if d$d$ is a positive integer, let Qd$Q_d$ be the set of prime powers coprime to d!$d!$ and let P(d,q ...
Derek Garton
wiley   +1 more source

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
doaj  

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
doaj   +1 more source

Explicit height estimates for CM curves of genus 2

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract In this paper, we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM and potentially good reduction outside a predefined set of primes. We also simplify some of the arguments.
Linda Frey, Samuel Le Fourn, Elisa Lorenzo García   +2 more
wiley   +1 more source

On local Galois deformation rings: generalised tori

Forum of Mathematics, Sigma
We 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
doaj   +1 more source

Topological K‐theory of quasi‐BPS categories for Higgs bundles

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract In a previous paper, we introduced quasi‐BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi‐BPS categories (called BPS in this case) are noncommutative analogues of Hitchin integrable systems.
Tudor Pădurariu, Yukinobu Toda
wiley   +1 more source

Differential Galois Theory and Hopf Algebras for Lie Pseudogroups

Axioms
According to a clever but rarely quoted or acknowledged work of E. Vessiot that won the prize of the Académie des Sciences in 1904, “Differential Galois Theory” (DGT) has mainly to do with the study of “Principal Homogeneous Spaces” (PHSs) for finite ...
Jean-Francois Pommaret
doaj   +1 more source

On the section conjecture over fields of finite type

Mathematische Nachrichten, Volume 298, Issue 11, Page 3476-3493, November 2025.
Abstract Assume that the section conjecture holds over number fields. We prove then that it holds for a broad class of curves defined over finitely generated extensions of Q$\mathbb {Q}$. This class contains every projective, hyperelliptic curve, every hyperbolic, affine curve of genus ≤2$\le 2$, and a basis of open subsets of any curve.
Giulio Bresciani
wiley   +1 more source

Rough sets based on Galois connections

International Journal of Applied Mathematics and Computer Science, 2020
Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one.
Madrid Nicolás, Medina Jesús, Ramírez-Poussa Eloísa   +2 more
doaj   +1 more source