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Linear codes over finite chain rings

Nettet6. des. 2024 · Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their … Nettet10. apr. 2024 · The primary goal of this article is to study the structural properties of cyclic codes over a finite ring R=Fq[u1,u2]/ u12−α2,u22−&beta ;2,u1u2−u2u1 ... linear code over F q for 1 ... Islam, H.; Prakash, O. Construction of LCD and new quantum codes from cyclic codes over a finite non chain ring. Cryptogr. Commun. 2024, 14 ...

ADDITIVE CYCLIC CODES OVER FINITE COMMUTATIVE CHAIN RINGS

NettetThe structure of linear and constacyclic codes over complete local principal ideal rings over CDVRs is obtained. The theory of linear codes over finite rings has been generalized to linear codes over infinite rings in two special cases; the ring of \begin{document}$ p $\end{document} -adic integers and formal power series ring. … Nettet29. aug. 2024 · It has been recently shown that if C and D are both 2-sided group codes over a finite field, then C and D^\bot are permutation equivalent. Hence the security … general cleaners south hadley https://gcprop.net

Galois correspondence on linear codes over finite chain …

NettetCodes over rings have been of interest in the last quarter after the discovery that some linear codes over Z 4 are related to non-linear codes over finite fields (see, for example, [6, 5, 11, 17, 18]). The first family of the rings used in this perspective was Zpn, where pis a prime and nis a positive integer. Nettet3. feb. 2016 · Galois Correspondence on Linear Codes over Finite Chain Rings. A. Fotue Tabue, E. Martínez-Moro, C. Mouaha. Given a finite Galois extension of finite … Nettet11. apr. 2024 · Under suitable conditions, linear codes over finite chain rings that are $\sigma$-LCD codes are characterized. Then we provide a necessary and sufficient … dead sea water source

$\sigma-$ LCD codes over finite chain rings-华中师范大学数学 …

Category:(PDF) Torsion Codes over a Finite Chain Rings - ResearchGate

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Linear codes over finite chain rings

Galois hulls of cyclic serial codes over a finite chain ring - arXiv

NettetNoncatastrophic encoders are an important class of polynomial generator matrices of convolutional codes. When these polynomials have coefficients in a finite field, these encoders have been characterized as polynomial left prime matrices. In this Nettet11. apr. 2024 · Hermitian duality of left dihedral codes over finite fields. 曹永林教授，硕士研究生导师。. 最初从事代数半群和偏序半群理论研究，现从事代数编码理论和信息安全研究。. 1980 年 12 月毕业于山东理工大学（原淄博师范专科学校）数学专业并留校任教至今。. 1987 年 7 月山东 ...

Linear codes over finite chain rings

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NettetWe generalise structure theorems of Calderbank and Sloane for linear and cyclic codes over ℤ pa to a finite chain ring. Our results are more detailed On the Structure of … Nettet1. apr. 2024 · Kai and Zhu [29] later proposed a method for generating quantum codes using cyclic codes of odd length over the finite chain ring F 4 + v F 4 with u 2 = 0. Further, Qian [18] has introduced a method for generating quantum error-correcting codes using cyclic codes over the finite non-chain ring F 2 + v F 2 with arbitrary length v 2 = v.

Nettet24. mar. 2024 · A linear code over a finite field with q elements F_q is a linear subspace C subset F_q^n. The vectors forming the subspace are called codewords. When … NettetCodes over finite rings have been known for several decades, but interest in these codes increased substantially after a break-through work by Hammons et al. in 1994, which shows that some well known binary non-linear codes like Kerdock codes and Preparata codes can be constructed from linear codes over ℤ 4 .

http://maths.ccnu.edu.cn/info/1045/28050.htm Nettet15. sep. 2024 · In this work, we first prove a necessary and sufficient condition for a pairs of linear codes over finite rings to be linear complementary pairs (abbreviated to …

http://maths.ccnu.edu.cn/info/1045/28048.htm

NettetA linear code C over the ring ℤ 15 is a additive sub-module. For every code word x = ( x 1, x 2, ⋯, x n) and y = ( y 1, y 2, ⋯, y n) in C, the inner product of x and y is defined as 〈 … dead sea where is it locatedNettet17. jun. 2024 · In this work, we extend the results to the finite non chain ring \mathcal {R} =\mathbb {F}_q+u\mathbb {F}_q+v\mathbb {F}_q+uv\mathbb {F}_q, where u^2=u,v^2=v and uv=vu . We define a correspondence between l -Galois dual of linear codes over \mathcal {R} and l -Galois dual of its component codes over \mathbb {F}_q . general cleaning operative jobsdead sea wholesalehttp://www.kurims.kyoto-u.ac.jp/EMIS/journals/EJC/Volume_7/PDF/v7i1r11.pdf general cleaning abu dhabiNettet1. apr. 2024 · We examine cyclic codes over a finite commutative non-chain ring ℛ = F q [ u, v] / 〈 u 2 − γ u, v 2 − ϵ v, u v − v u 〉 for γ, ϵ ∈ F q * and its relevance in the generation of optimal LCD codes and comparatively new quantum codes. It is worth noting that the ring in [21] is a specific form of our fundamental ring ℛ (for γ ... general cleaning comicNettet2.2. Codes over chain rings A linear code Cof length nover the ring Ris defined to be a submodule of the R-module Rn. We will denote by f0g, the zero-submodule where 0 = (0;0;:::;0) 2Rn. A linear code Cover Ris free if C˘=Rkas R-modules for some positive integer k. The residue code of a linear code Cover Ris the linear code ˇ(C) over F q ˇ ... dead sea water depthNettetPatrick Sole, in Codes and Rings, 2024. 4.2.1 Linear Codes and Geometries over Finite Frobenius Rings. Let R denote a finite ring. A left linear code of length n over R is a … dead sea wholesale products