Linear codes over finite chain rings

Author: revf

August undefined, 2024

http://www.kurims.kyoto-u.ac.jp/EMIS/journals/EJC/Volume_7/PDF/v7i1r11.pdf 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 …

On the Hamming distance of linear codes over a finite chain ring

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 ... Nettet1. aug. 2024 · Linear Algebra on finite rings allows for stronger statements than possible for the class of rings in general. This is based on purely combinatorial arguments. Remark 1 Let be a finite ring and let be a positive integer. For an -element subset of the following are equivalent: (a) is a basis of . (b) is linearly independent in . (c) dol registered apprenticeship program

Bounds on covering radius of linear codes with Chinese Euclidean ...

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 applications in cryptography, in the context of side-channel and fault injection attacks. The security parameter for an LCP of codes is defined as the minimum of the minimum … 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 Nettet13. 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 … dols brighton and hove

Linear and Cyclic Codes over direct product of Finite Chain Rings

On the Construction of Quantum and LCD Codes from Cyclic Codes over …

Nettet19. 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 … Nettet2.2. 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 ... fake number sms indiaNettetCodes 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. fake number on whatsapp

"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 〈 … " - Linear codes over finite chain rings

Linear codes over finite chain rings

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 … 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 .

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Nettetpolycyclic codes over Galois rings was established. Also in [4] some class of constacyclic codes over nite chain rings were characterized via cyclotomic cosets as contraction of … Nettet1. aug. 2024 · Linear codes over finite rings are described here as trace codes for a suitable generalization of the trace called a GF-trace. Cyclic codes over Galois rings …

Nettet1. nov. 2024 · Liu XSLiu H σ - LCD codes over finite chain ringsDes. Codes Cryptogr.202488727 74610.1007/s10623-019-00706-w 19. Liu ZWang JLinear complementary dual codes over ringsDes. Codes Cryptogr.2024873077 308610.1007/s10623-019-00664-3 20. MacWilliams FJSloane NJAThe theory of error … Nettetpolycyclic codes over Galois rings was established. Also in [4] some class of constacyclic codes over nite chain rings were characterized via cyclotomic cosets as contraction of some cyclic codes. In [11], the authors studied the algebraic structure of a class of linear codes over nite chain rings containing the polycyclic codes.

Nettet1. des. 2024 · In this paper, we first generalize the l-linear intersection pair (l-LIP) of codes over finite fields to the linear l-intersection pair of codes over finite chain rings. … Nettet1. des. 2024 · The purpose of this paper is to introduce the critical exponent for linear codes over finite rings which is analogous to that for representable matroids over F …

Nettet1. aug. 2004 · This work generalises structure theorems of Calderbank and Sloane for linear and cyclic codes over ℤpa to a finite chain ring and uses non-trivial results from Commutative Algebra. 270 Negacyclic codes over Z4 of even length Thomas Blackford Computer Science IEEE Trans. Inf. Theory 2003 TLDR

Nettet31. jul. 2012 · Torsion codes over residue fields of finite chain rings are introduced, and some of their properties are drived. Finally, we show that there are no non-trivial M DR … fake numbers that workNettetNoncatastrophic 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 fake numbers in mathNettetThe 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. … dols cheshire eastNettet1. feb. 2024 · Galois invariance for linear codes over finite chain rings A matrix G is generator matrix for the code B ⊂ S n if the rows of G span B and none of them can be written as a linear combination of the remaining rows. The rows of an arbitrary generator matrix for B form S -basis of B. fake numbers that work for discordhttp://maths.ccnu.edu.cn/info/1045/28050.htm dols central bedfordshireNettet10. 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 ... fake numbers to give to scammersNettet3. 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 … fake numbers to give out