Results 141 to 150 of about 330 (178)

Conversion of Element Representations in Galois Rings

Mathematics in Computer Science, 2020
Let \(G(p^s,m)\) be a Galois ring. Each element in \(G(p^s,m)\) has an additive representation and a \(p\)-adic representation. In this paper, the authors develops a series of programs allowing the convertion between these two representations in a Galois ring.
Juan Carlos Ku-Cauich, Guillermo Morales-Luna   +1 more
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Nonassociative Galois rings

Discrete Mathematics and Applications, 2002
Abstract The aim of this paper is to introduce the notion of a generalised Galois ring, that is, a Galois ring without associativity assumptions. Some basic properties of associative Galois rings such as cardinality, characteristic, and ideal lattice structure are extended to the nonassociative case.
González, S., Markov, V. T., Martínez, C., Nechaev, A. A., Rúa, I. F.   +4 more
openaire   +2 more sources

Decomposition of Witt Rings and Galois Groups

Canadian Journal of Mathematics, 1995
AbstractTo each fieldFof characteristic not 2, one can associate a certain Galois group 𝒢F, the so-calledW-group ofF, which carries essentially the same information as the Witt ringW(F)ofF. In this paper we show that direct products of Witt rings correspond to free products of these Galois groups (in the appropriate category), group ring construction ...
Mináč, Ján, Smith, Tara L.
openaire   +2 more sources

Galois Fields and Galois Rings Made Easy

2017
International ...
openaire   +3 more sources

The Generalized Center Galois Extensions of Rings

Southeast Asian Bulletin of Mathematics, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Szeto, George, Xue, Lianyong
openaire   +2 more sources

Galois and Quasi-Galois Rings: Structure and Properties

2002
In this chapter we firstly want to analyze the structure of Galois rings which are, in our terminology, Galois extensions of local rings of the form \( {Z_p}n \), where p is a prime and n a positive integer. The importance of such rings is mainly due to the following facts: 1.
Gilberto Bini, Flaminio Flamini
openaire   +1 more source

COORDINATE SETS OF GENERALIZED GALOIS RINGS

Journal of Algebra and Its Applications, 2004
A Generalized Galois Ring (GGR) S is a finite nonassociative ring with identity of characteristic pn, for some prime number p, such that its top-factor [Formula: see text] is a semifield. It is well-known that if S is an associative Galois Ring (GR), then it contains a multiplicatively closed subset isomorphic to [Formula: see text], the so-called ...
González, S., Martínez, C., Rúa, I. F., Markov, V. T., Nechaev, A. A.   +4 more
openaire   +2 more sources

On The Centralizer Of A Galois Ring.

1963
PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/185929/2/6400851 ...
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Cyclic Codes over Galois Rings

2016
Let R be a Galois ring of characteristic $$p^a$$, where p is a prime and a is a natural number. In this paper cyclic codes of arbitrary length n over R have been studied. The generators for such codes in terms of minimal degree polynomials of certain subsets of codes have been obtained.
Jasbir Kaur, Sucheta Dutt, Ranjeet Sehmi
openaire   +1 more source

Galois Rings and Pseudo-random Sequences

2007
We survey our constructions of pseudo random sequences (binary, Z8, Z2l,...) from Galois rings. Techniques include a local Weil bound for character sums, and several kinds of Fourier transform. Applications range from cryptography (boolean functions, key generation), to communications (multi-code CDMA), to signal processing (PAPR reduction).
Patrick Solé, Dmitrii V. Zinoviev
openaire   +1 more source