Results 1 to 10 of about 3,398,533 (269)

Finite Commutative Chain Rings [PDF]

Finite Fields and Their Applications, 2001
A commutative ring with unit is called a chain ring if all its ideals form a chain under inclusion. All finite chain rings can be obtained in the following way: Let \(p\) be a prime, \(n,r>0\), \(f\in \mathbb{Z}_{p^n}[X]\) a monic polynomial, \(\deg(f)=r\) whose image in \(\mathbb{Z}_p[X]\) is irreducible and let \(\text{GR} (p^n,r): =\mathbb{Z}_{p^n ...
Hou, Xiang-dong, Xiang-dong Hou
exaly   +3 more sources

On Automorphism Groups of Finite Chain Rings [PDF]

Symmetry, 2021
A finite ring with an identity is a chain ring if its lattice of left ideals forms a unique chain. Let R be a finite chain ring with invaraints p,n,r,k,k′,m. If n=1, the automorphism group Aut(R) of R is known. The main purpose of this article is to study the structure of Aut(R) when n>1. First, we prove that Aut(R) is determined by the automorphism
Yousef Alkhamees, Sami Alabiad
exaly   +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

On polycyclic codes over a finite chain ring

Advances in Mathematics of Communications, 2020
Galois images of polycyclic codes over a finite chain ring $S$ and their annihilator dual are investigated. The case when a polycyclic codes is Galois-disjoint over the ring $S,$ is characterized and, the trace codes and restrictions of free polycyclic codes over $S$ are also determined givind an analogue of Delsarte theorem among trace map, any S ...
Edgar Martínez-Moro
exaly   +6 more sources

Communication Over Finite-Chain-Ring Matrix Channels [PDF]

IEEE Transactions on Information Theory, 2014
Submitted to IEEE Transactions on Information Theory, April 2013. Revised version submitted in Feb. 2014.
Danilo Silva, Frank Kschischang, Chen Feng   +2 more
exaly   +6 more sources

Skew constacyclic codes over finite chain rings

Advances in Mathematics of Communications, 2012
Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of $x^n-λ$, where $λ$ is a unit element, are exhibited.
San Ling, Patanee Udomkavanich, Somphong Jitman   +2 more
exaly   +3 more sources

On Double Cyclic Codes over Finite Chain Rings for DNA Computing [PDF]

Entropy
Let e be a fixed positive integer and n1,n2 be odd positive integers. The main objective of this article is to investigate the algebraic structure of double cyclic codes of length (n1,n2) over the finite chain ring Re = F4e+vF4e, where v2=0.
Shakir Ali, Amal S. Alali, Mohd Azeem, Atif Ahmad Khan, Kok Bin Wong   +4 more
doaj   +2 more sources

MDS and MHDR Cyclic Codes over Finite Chain Rings

Journal of Mathematics
This work establishes a unique set of generators for a cyclic code over a finite chain ring. Towards this, we first determine the minimal spanning set and rank of the code.
Monika Dalal, Sucheta Dutt, Ranjeet Sehmi   +2 more
doaj   +4 more sources

Left dihedral codes over finite chain rings [PDF]

Discrete Mathematics, 2022
Let $R$ be a finite commutative chain ring, $D_{2n}$ be the dihedral group of size $2n$ and $R[D_{2n}]$ be the dihedral group ring. In this paper, we completely characterize left ideals of $R[D_{2n}]$ (called left $D_{2n}$-codes) when ${\rm gcd}(char(R),n)=1$. In this way, we explore the structure of some skew-cyclic codes of length 2 over $R$ and also
H. Aghili, R. Sobhani
openaire   +5 more sources

Linear Codes over Finite Chain Rings [PDF]

The Electronic Journal of Combinatorics, 1999
The aim of this paper is to develop a theory of linear codes over finite chain rings from a geometric viewpoint. Generalizing a well-known result for linear codes over fields, we prove that there exists a one-to-one correspondence between so-called fat linear codes over chain rings and multisets of points in projective Hjelmslev geometries, in the ...
Thomas Honold, Ivan N. Landjev
openaire   +3 more sources