Results 31 to 40 of about 2,481 (228)

Discrete Cartesian Coordinate Transformations: Using Algebraic Extension Methods

Applied Sciences
It is shown that it is reasonable to use Galois fields, including those obtained by algebraic extensions, to describe the position of a point in a discrete Cartesian coordinate system in many cases. This approach is applicable to any problem in which the
Aruzhan Kadyrzhan, Dinara Matrassulova, Yelizaveta Vitulyova, Ibragim Suleimenov   +3 more
doaj   +1 more source

NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOIS

Системный анализ и прикладная информатика, 2017
Further development of cryptographic algorithms based on the principles of many-valued logic requires more accurate research of non-binary cryptographic primitives – S-boxes.
A. V. Sokolov, O. N. Zhdanov
doaj   +1 more source

Chebotarev's theorem for cyclic groups of order pq$pq$ and an uncertainty principle

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3841-3856, December 2025.
Abstract Let p$p$ be a prime number and ζp$\zeta _p$ a primitive p$p$th root of unity. Chebotarev's theorem states that every square submatrix of the p×p$p \times p$ matrix (ζpij)i,j=0p−1$(\zeta _p^{ij})_{i,j=0}^{p-1}$ is nonsingular. In this paper, we prove the same for principal submatrices of (ζnij)i,j=0n−1$(\zeta _n^{ij})_{i,j=0}^{n-1}$, when n=pr ...
Maria Loukaki
wiley   +1 more source

A Method for Strict Remote User Identification Using non - Reversible Galois Field Transformations

MATEC Web of Conferences, 2017
This article proposes an approach that accelerates the realization of strict remote user identification using non reversible Galois field transformation.
Bardis Nikolaos G., Markovskyi Oleksandr P., Doukas Nikolaos   +2 more
doaj   +1 more source

A note on the cohomology of moduli spaces of local shtukas

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3709-3729, December 2025.
Abstract We study localized versions of spectral action of Fargues–Scholze, using methods from higher algebra. As our main motivation and application, we deduce a formula for the cohomology of moduli spaces of local shtukas under certain genericity assumptions, and discuss its relation with the Kottwitz conjecture.
David Hansen, Christian Johansson
wiley   +1 more source

Computation of Hilbert sequence for composite quadratic extensions using different type of primes in Q

International Journal of Mathematics and Mathematical Sciences, 1997
First, we will give all necessary definitions and theorems. Then the definition of a Hilbert sequence by using a Galois group is introduced. Then by using the Hilbert sequence, we will build tower fields for extension K/k, where K=k(d1,d2) and k=Q for ...
M. Haghighi, J. Miller
doaj   +1 more source

Design space exploration of high throughput finite field multipliers for channel coding on Xilinx FPGAs [PDF]

Advances in Radio Science, 2012
Channel coding is a standard technique in all wireless communication systems. In addition to the typically employed methods like convolutional coding, turbo coding or low density parity check (LDPC) coding, algebraic codes are used in many cases.
C. de Schryver, S. Weithoffer, U. Wasenmüller, N. Wehn   +3 more
doaj   +1 more source

Iitaka fibrations and integral points: A family of arbitrarily polarized spherical threefolds

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract Studying Manin's program for a family of spherical log Fano threefolds, we determine the asymptotic number of integral points whose height associated with an arbitrary ample line bundle is bounded. This confirms a recent conjecture by Santens and sheds new light on the logarithmic analog of Iitaka fibrations, which have not yet been adequately 
Ulrich Derenthal, Florian Wilsch
wiley   +1 more source

Quadratic subfields on quartic extensions of local fields

International Journal of Mathematics and Mathematical Sciences, 1988
We show that any quartic extension of a local field of odd residue characteristic must contain an intermediate field. A consequence of this is that local fields of odd residue characteristic do not have extensions with Galois group A4 or S4 ...
Joe Repka
doaj   +1 more source

The m$m$‐step solvable anabelian geometry of mixed‐characteristic local fields

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract Let K$K$ be a mixed‐characteristic local field. For an integer m⩾0$m \geqslant 0$, we denote by Km/K$K^m / K$ the maximal m$m$‐step solvable extension of K$K$, and by GKm$G_K^m$ the maximal m$m$‐step solvable quotient of the absolute Galois group GK$G_K$ of K$K$.
Seung‐Hyeon Hyeon
wiley   +1 more source