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Some Constacyclic Codes over Finite Chain Rings [PDF]
Advances in Mathematics of Communications, 2012 For $\lambda$ an $n$-th power of a unit in a finite chain ring we prove that $\lambda$-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.
Batoul, Aicha +2 more
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Communication over Finite-Chain-Ring Matrix Channels [PDF]
IEEE Transactions on Information Theory, 2014 Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over certain finite rings, more efficient physical-layer network coding schemes can be ...
Feng, Chen +3 more
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On classification of finite commutative chain rings
AIMS Mathematics, 2022 Let $ R $ be a finite commutative chain ring with invariants $ p, n, r, k, m. $ It is known that $ R $ is an extension over a Galois ring $ GR(p^n, r) $ by an Eisenstein polynomial of some degree $ k $.
Sami Alabiad, Yousef Alkhamees
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On Multiplicative Matrix Channels over Finite Chain Rings [PDF]
Journal of Communication and Information Systems, 2013 Motivated by physical-layer network coding, this paper considers communication in multiplicative matrix channels over finite chain rings. Such channels are defined by the law $Y =A X$, where $X$ and $Y$ are the input and output matrices, respectively ...
Feng, Chen +3 more
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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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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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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
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AIMS Mathematics, 2022 An associative Artinian ring with an identity is a chain ring if its lattice of left (right) ideals forms a unique chain. In this article, we first prove that for every chain ring, there exists a certain finite commutative chain subring which ...
Yousef Alkhamees, Sami Alabiad
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Structure of a chain ring as a ring of matrices over a Galois ring
AIMS Mathematics, 2022 The structure of a finite chain ring has already been described by Wirt in 1972 and others later. The purpose of this article is to describe another structure of a finite chain ring as a ring of square matrices over Galois ring using the companion matrix
Yousef Alkhamees, Badr Alhajouj
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Skew Constacyclic Codes over Finite Fields and Finite Chain Rings [PDF]
Mathematical Problems in Engineering, 2016 This paper overviews the study of skewΘ-λ-constacyclic codes over finite fields and finite commutative chain rings. The structure of skewΘ-λ-constacyclic codes and their duals are provided. Among other results, we also consider the Euclidean and Hermitian dual codes of skewΘ-cyclic and skewΘ-negacyclic codes over finite chain rings in general and ...
Dinh, Hai Q. +2 more
openaire +3 more sources