Results 11 to 20 of about 158,948 (278)

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
openaire   +2 more sources

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., Álvarez-García C.   +1 more
doaj   +1 more source

Density of free modules over finite chain rings

Linear Algebra and its Applications, 2022
In this paper we focus on modules over a finite chain ring $\mathcal{R}$ of size $q^s$. We compute the density of free modules of $\mathcal{R}^n$, where we separately treat the asymptotics in $n,q$ and $s$. In particular, we focus on two cases: one where we fix the length of the module and one where we fix the rank of the module.
Eimear Byrne, Anna-Lena Horlemann, Karan Khathuria, Violetta Weger   +3 more
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Symbol-Triple Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over ${\mathbb{F}}_q+u{\mathbb{F}}_q+u^2{\mathbb{F}}_q$

Mathematics, 2022
Let p be an odd prime, where ϑ and m are positive integers. Let ψ be a nonzero element of the finite field Fq, where q=pm, and R=Fq+uFq+u2Fq(u3=0). In this paper, we determine completely the symbol-triple distances of all ψ-constacyclic codes of length ...
Hai Q. Dinh, Jamal Laaouine, Brahim Boudine, Woraphon Yamaka   +3 more
doaj   +1 more source

Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established ...
Castillo-Guillén C. A., Álvarez-García C.   +1 more
doaj   +1 more source

On skew cyclic codes over $ M_{2}(\mathbb{F}_{2}) $

AIMS Mathematics, 2023
The algebraic structure of skew cyclic codes over $ M_{2} $($ \mathbb{F}_2 $), using the $ \mathbb{F}_4 $-cyclic algebra, is studied in this work. We determine that a skew cyclic code with a polynomial of minimum degree $ d(x) $ is a free code generated ...
Xuesong Si, Chuanze Niu
doaj   +1 more source

Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over \({{\mathbb{F}_{p^m}[u]}/{\langle u^3\rangle}}\)

Mathematics, 2021
Let p be a prime, s, m be positive integers, γ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/⟨u3⟩ be the finite commutative chain ring.
Mohammed E. Charkani, Hai Q. Dinh, Jamal Laaouine, Woraphon Yamaka   +3 more
doaj   +1 more source

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., Rentería-Márquez C.   +1 more
doaj   +1 more source

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
openaire   +1 more source

Repeated-root cyclic and negacyclic codes over a finite chain ring [PDF]

, 2005
We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2.
Berg, R. van den, Berkhemer, O.A., Dippel, D.W.J., Jansen, I.G.H., Lingsma, H.F., Lugt, A. van der, Majoie, C.B.L.M., Marquering, H.A., MR CLEAN Trial Investigators, Oostenbrugge, R.J. van, Roos, Y.B.W.E.M., Slump, C.H., Treurniet, K.M., Vuuren, A.B. van, Walderveen, M.A.A. van, Wijngaard, I.R. van den, Zwam, W.H. van   +16 more
core   +6 more sources