Results 21 to 30 of about 226,788 (288)
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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MDS and MHDR cyclic codes over finite chain rings [PDF]
Journal of mathematics, 2023 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, R. Sehmi
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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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Convolutional codes over finite chain rings, MDP codes and their characterization [PDF]
Advances in Mathematics of Communications, 2021 In this paper, we develop the theory of convolutional codes over finite commutative chain rings. In particular, we focus on maximum distance profile (MDP) convolutional codes and we provide a characterization of these codes, generalizing the one known ...
Gianira N. Alfarano +3 more
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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 ...
Honold, Thomas, Landjev, Ivan
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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 constructed. This paper considers the problem of communication over a finite-ring matrix channel $Y = AX +
Feng, Chen +3 more
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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.
Sami Alabiad, Yousef Alkhamees
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Decoding Linear Codes over Chain Rings Given by Parity Check Matrices
Mathematics, 2021 We design a decoding algorithm for linear codes over finite chain rings given by their parity check matrices. It is assumed that decoding algorithms over the residue field are known at each degree of the adic decomposition.
José Gómez-Torrecillas +2 more
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Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 The family of finite local Frobenius non-chain rings of length 5 and nilpotency index 4 is determined, as a by-product all finite local Frobenius non-chain rings with p5 elements (p a prime) and nilpotency index 4 are given.
Castillo-Guillén C. A. +1 more
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DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established.
Castillo-Guillén C. A. +1 more
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