Results 21 to 30 of about 143,950 (277)
Bounds for Coding Theory over Rings
Entropy, 2022 Coding theory where the alphabet is identified with the elements of a ring or a module has become an important research topic over the last 30 years. It has been well established that, with the generalization of the algebraic structure to rings, there is a need to also generalize the underlying metric beyond the usual Hamming weight used in traditional
Gassner, Niklas +3 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 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 finite ...
Mo Elisa, Armand MarcA
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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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p-Adic estimates of Hamming weights in Abelian codes over Galois rings [PDF]
, 2006 A generalization of McEliece's theorem on the p-adic valuation of Hamming weights of words in cyclic codes is proved in this paper by means of counting polynomial techniques introduced by Wilson along with a technique known as trace-averaging introduced ...
Katz, Daniel J.
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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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CYCLIC CODES OVER SOME SPECIAL RINGS [PDF]
Bulletin of the Korean Mathematical Society, 2013 In this paper we will study cyclic codes over some special rings: F_{q}[u]/(u^{i}), F_{q}[u_1,...u_{i}]/(u_1^2,u_2^2,...,u_{i}^2, u_1 u_2 - u_2 u_1,...,u_{i}u_{j} - u_{j}u_{i},...), F_{q}[u,v]/(u^{i},v^{j},uv-vu), q=p^{r}, where p is a prime number, r\in N-{0} and F_{q} is a field with q elements.
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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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Self-Dual and Complementary Dual Abelian Codes over Galois Rings [PDF]
, 2019 Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications.
Jitman, Somphong, Ling, San
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