Results 11 to 20 of about 3,045,703 (258)
γ-Dual Codes over Finite Commutative Chain Rings
AxiomsIn this article, the notion of γ-dual codes over finite chain rings is introduced as an extension of dual codes over finite chain rings. Various characteristics and properties of γ-dual codes over finite chain rings are explored.
Hai Q. Dinh +2 more
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Enumeration of finite commutative chain rings [PDF]
Journal of Algebra, 1973 AbstractA chain ring is an associative, commutative ring with an identity whose ideals form a chain. We associate with each finite chain ring five invariants (integers) and determine (in certain cases) the number of isomorphism classes of rings with given invariants.
Clark, W.Edwin, Liang, Joseph J
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, 1970 The theory of near-rings has arisen in a variety of ways. There is a natural desire to generalise the theory of rings and skew fields by relaxing some of their defining axioms.
Holcombe, William Michael Lloyd
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On Automorphism Groups of Finite Chain Rings [PDF]
Symmetry, 2021 A finite ring with an identity is a chain ring if its lattice of left ideals forms a unique chain. Let R be a finite chain ring with invaraints p,n,r,k,k′,m. If n=1, the automorphism group Aut(R) of R is known. The main purpose of this article is to study the structure of Aut(R) when n>1. First, we prove that Aut(R) is determined by the automorphism
Sami Alabiad, Yousef Alkhamees
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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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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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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 ...
Thomas Honold, Ivan N. Landjev
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On the Density of Codes over Finite Chain Rings
2023 IEEE Information Theory Workshop (ITW), 2023 We determine the asymptotic proportion of free modules over finite chain rings with good distance properties and treat the asymptotics in the code length n and the residue field size q separately. We then specialize and apply our technique to rank metric codes and to Hamming metric codes.
Anna-Lena Horlemann +2 more
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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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Expanders on matrices over a finite chain ring, I
International Journal of Mathematics, 2023 In this work and its sequel, we study the expanding phenomenon of matrices over a finite chain ring of large residue field. A sum-product estimate is proved. It is shown that [Formula: see text] is a moderate expander on [Formula: see text] matrices with exponent [Formula: see text].
Dung M. Ha, Hieu T. Ngo
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