Linear codes over finite chain rings
Nettet17. 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 . NettetWe introduce a new type of linear and cyclic codes. These codes are defined over a direct product of 2 finite chain rings. The definition of these codes as certain …
Linear codes over finite chain rings
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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 … NettetPatrick 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 …
http://maths.ccnu.edu.cn/info/1045/28050.htm Nettet14. des. 2024 · A NOTE ON k-GALOIS LCD CODES OVER THE RING - Volume 104 Issue 1. ... Liu, H. and Pan, X., ‘ Galois hulls of linear codes over finite fields ’, Des. Codes Cryptogr. 88 ... Liu, X. and Liu, H., ‘ LCD codes over finite chain rings ’, Finite Fields Appl. 34 (2015), 1 ...
NettetIn coding theory, quasi-twisted (QJ) codes form an important class of codes which has been extensively studied. We decompose a QT code to a direct sum of component codes - linear codes over rings. Fu 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. …
Nettet14. apr. 2024 · PDF On Apr 14, 2024, Karima Chatouh published Skew cyclic Linear codes over 𝑹 = 𝑅 + 𝑤𝑅 + 𝑤2𝑅 Find, read and cite all the research you need on ResearchGate
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 〈 … mobility scooters for sale ontarioNettetTHE WEIGHT DISTRIBUTION OF CODES OVER FINITE CHAIN RINGS 3 3. Generalities on linear codes over finite chain rings A finite ring with unity 1 6= 0 is called a left (resp. right) chain ring if its left (resp. right) ideals are linearly ordered by inclusion. Note that a finite chain ring is a local ring where all the ideals are principal. mobility scooters for sale northern irelandNettet4. jul. 2016 · These codes are defined over a direct product of two finite chain rings. The definition of these codes as certain submodules of the direct product of copies of these rings is given... mobility scooters for sale in south shieldsNettetNoncatastrophic 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 mobility scooters for sale niNettet19. nov. 2024 · More recently, a necessary and sufficient condition for a pair of linear codes over finite chain rings to be LCP of codes has been established by Hu and Liu … mobility scooters for sale melbourneNettet13. apr. 2024 · Projective Hjelmslev geometries are an important tool for the investigation of linear codes over finite chain rings. It is known that linear codes over finite chain rings that are regular (i.e. the entries in no coordinate position are entirely contained in … ink sans fight infinite hpNettet2.2. 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 ... mobility scooters for sale near kissimmee