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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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IEEE Access, 2023 A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this integer residue ring which is closed under the action of constant multiplication by the Gaussian or Eisenstein integers. In this paper, we define
Hajime Matsui
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On the Covering Radius of Codes over Zpk
Mathematics, 2020 In this correspondence, we investigate the covering radius of various types of repetition codes over Z p k ( k ≥ 2 ) with respect to the Lee distance.
Mohan Cruz +2 more
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Structured LDPC Codes over Integer Residue Rings
EURASIP Journal on Wireless Communications and Networking, 2008 This paper presents a new class of low-density parity-check (LDPC) codes over ℤ2a represented by regular, structured Tanner graphs. These graphs are constructed using Latin squares defined over a multiplicative group of a Galois ring, rather than a ...
Marc A. Armand, Elisa Mo
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Linear codes and cyclic codes over finite rings and their generalizations: a survey
Electronic Journal of Graph Theory and Applications, 2023 We survey a recent progress of cyclic codes over finite rings and their generalization to skew cyclic as well as skew cyclic codes with derivation over finite rings, focusing on structural properties of the codes.
Djoko Suprijanto
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Linear Codes over Finite Rings
Trends in Computational and Applied Mathematics, 2005 In this paper we present a construction technique of cyclic, BCH, alternat, Goppa and Srivastava codes over a local finite commutative rings with identity.
A.A. de Andrade, R. Palazzo Jr.
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Constacyclic Codes over Finite Chain Rings of Characteristic p
Axioms, 2021 Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study λ-constacyclic codes of an arbitrary length N over R, where λ is a unit of R.
Sami Alabiad, Yousef Alkhamees
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Duality of Codes Over Non-Unital Rings of Order Four
IEEE Access, 2023 In this paper, we present a basic theory of the duality of linear codes over three of the non-unital rings of order four; namely $I$ , $E$ , and $H$ as denoted in (Fine, 1993).
Adel Alahmadi +2 more
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Matrix-Product Codes over Commutative Rings and Constructions Arising from σ,δ-Codes
Journal of Mathematics, 2021 A well-known lower bound (over finite fields and some special finite commutative rings) on the Hamming distance of a matrix-product code (MPC) is shown to remain valid over any commutative ring R.
Mhammed Boulagouaz, Abdulaziz Deajim
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On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
Mathematics, 2021 In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings.
Ángel Luis Muñoz Castañeda +2 more
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