Results 1 to 10 of about 3,045,703 (258)
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
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Determinants of some special matrices over commutative finite chain rings
Special Matrices, 2020 Circulant matrices over finite fields and over commutative finite chain rings have been of interest due to their nice algebraic structures and wide applications. In many cases, such matrices over rings have a closed connection with diagonal matrices over
Jitman Somphong
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On Double Cyclic Codes over Finite Chain Rings for DNA Computing [PDF]
EntropyLet 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 +4 more
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Open and Periodic Boundary Conditions in Statistical Mechanics: A Case Study of the Antiferromagnetic Ising Chain [PDF]
EntropyThe transfer-matrix method is employed to investigate a spin-1/2 Ising chain under open and periodic boundary conditions. It is demonstrated that finite-size Ising chains with antiferromagnetic coupling may exhibit significantly distinct magnetic ...
Katarína Karl’ová, Jozef Strečka
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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 +2 more
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Some constacyclic codes over finite chain rings
Advances in Mathematics of Communications, 2016 For $λ$ an $n$-th power of a unit in a finite chain ring we prove that $λ$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the $α+p β$-constacyclic codes of length $p^s$ over the Galois ring $GR(p^e,r)$.
Aaron Gulliver, Kenza Guenda
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On J-Diagrams for the One Groups of Finite Chain Rings
Symmetry, 2023 Let R be a finite commutative chain ring with invariants p,n,r,k,m. The purpose of this article is to study j-diagrams for the one group H=1+J(R) of R, where J(R)=(π) is Jacobson radical of R. In particular, we prove the existence and uniqueness of j-diagrams for such one group.
Yousef Alkhamees, Sami Alabiad
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Galois correspondence on linear codes over finite chain rings [PDF]
Discrete Mathematics, 2020 Given $\texttt{S}|\texttt{R}$ a finite Galois extension of finite chain rings and $\mathcal{B}$ an $\texttt{S}$-linear code we define two Galois operators, the closure operator and the interior operator. We proof that a linear code is Galois invariant if and only if the row standard form of its generator matrix has all entries in the fixed ring by the ...
Alexandre Fotue Tabue +1 more
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Determinants of tridiagonal matrices over some commutative finite chain rings
Special MatricesDiagonal matrices and their generalization in terms of tridiagonal matrices have been of interest due to their nice algebraic properties and wide applications.
Jitman Somphong, Sricharoen Yosita
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MDS and MHDR Cyclic Codes over Finite Chain Rings
Journal of MathematicsThis 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 +2 more
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