Results 1 to 10 of about 30,131 (212)

Polynomials with minimal value set over Galois rings [PDF]

International Journal of Mathematics and Mathematical Sciences, 1991
Let GR(pn,m) denote the Galois ring of order pn,m, where p is a prime. In this paper we define and characterize minimal value set polynomials over GR(pn,m).
Maria T. Acosta-De-Orozco, Javier Gomez-Calderon   +1 more
doaj   +2 more sources

Classification of Unit Groups of Five Radical Zero Completely Primary Finite Rings Whose First and Second Galois Ring Module Generators Are of the Order pk,k=2,3,4 [PDF]

Journal of Mathematics, 2022
Let R0=GRpkr,pk be a Galois maximal subring of  R  so that R=R0⊕U⊕V⊕W⊕Y, where U,V,W, and Y are R0/pR0 spaces considered as R0-modules, generated by the sets u1,⋯,ue,v1,⋯,vf,w1,⋯,wg, and y1,⋯,yh, respectively.
Hezron Saka Were, Maurice Owino Oduor
doaj   +2 more sources

The Galois theory of matrix $C$-rings [PDF]

Applied Categorical Structures, 2005
27 pages ...
Brzezinski, Tomasz, Turner, Ryan B.
openalex   +6 more sources

Proposal and Analysis of a Novel Class of PUFs Based on Galois Ring Oscillators

IEEE Access, 2020
In this article, the possibility of using Galois ring oscillators to construct physically unclonable functions (PUFs) has been studied. The idea is to use novel PUF architectures, similar as the ring oscillator PUFs that, instead of comparing frequencies,
Miguel Garcia-Bosque, Guillermo Diez-Senorans, Carlos Sanchez-Azqueta, Santiago Celma   +3 more
doaj   +3 more sources

Quantum Codes from Galois Hulls of Constacyclic Codes over a Finite Non-Chain Ring [PDF]

Entropy
We study the algebraic structures of constacyclic codes over a new finite non-chain ring R and their l-Galois dual codes based on a new Gray map ϕ and determine the dimensions of the l-Galois hull of constacyclic codes over R.
Enbin Zhang, Bo Kong, Xiying Zheng
doaj   +2 more sources

A Note on a Standard Model for Galois Rings [PDF]

Applicable Algebra in Engineering, Communication and Computing, 2021
Submitted to ...
E. Martínez Moro, Alejandro Piñera Nicolás, I. F. Rúa   +2 more
openalex   +4 more sources

Self-Dual Normal Basis of a Galois Ring [PDF]

Journal of Mathematics, 2014
Let R′=GR(ps,psml) and R=GR(ps,psm) be two Galois rings. In this paper, we show how to construct normal basis in the extension of Galois rings, and we also define weakly self-dual normal basis and self-dual normal basis for R′ over R, where R′ is ...
Irwansyah, Intan Muchtadi-Alamsyah, Aleams Barra, Ahmad Muchlis   +3 more
doaj   +2 more sources

Normal Bases on Galois Ring Extensions [PDF]

Symmetry, 2018
In this paper we study the normal bases for Galois ring extension ${{R}} / {Z}_{p^r}$ where ${R}$ = ${GR}$(pr, n). We present a criterion on normal basis for ${{R}} / {Z}_{p^r}$ and reduce this problem to one of finite field extension $\overline{R} / \overline{Z}_{p^r}=F_{q} / F_{p}  (q=p^n)$ by Theorem 1. We determine all optimal normal bases
Keqin Feng
exaly   +3 more sources

On Galois matrix rings of a ring

Gulf Journal of Mathematics, 2013
Let R be a ring with 1, Mn(R) the ring of n × n-matrices over R for an integer n, and G an inner automorphism group of Mn(R) of order n2 induced by {Ui ∈ Mn(R), i = 1, ... , n2}. Then the Galois matrix ring Mn(R) over R with inner Galois group G is characterized in terms of {Ui} and the trace of G.
George Szeto, Jiang Xiaolong
openalex   +3 more sources

A combinatory approach of non-chain ring and henon map for image encryption application [PDF]

Scientific Reports
Algebraic structures play a vital role in securing important data. These structures are utilized to construct the non-linear components of block ciphers.
Salman Mohi Ud Din, Tariq Shah, Fahad Alblehai, Sameer Nooh, Sajjad Shaukat Jamal   +4 more
doaj   +2 more sources