Linear codes over finite chain rings

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Nettet20. aug. 2024 · In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the … 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 …

Polyadic Cyclic Codes over a Non-Chain Ring

Nettet10. apr. 2024 · Codes over the Finite Commutative Rings Shakir Ali 1, * , Amal S. Alali 2 , Mohammad Jeelani 3 , Muhammet Kurulay 4 , Elif Segah Öztas 5 and Pushpendra Sharma 1 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 grayslake rehab services

NEW QUANTUM AND LCD CODES FROM CYCLIC CODES OVER A FINITE NON-CHAIN RING

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. 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 … 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 … choko health benefits

Linear codes over finite rings are trace codes - ScienceDirect

arXiv:2210.15436v2 [cs.IT] 28 Oct 2024

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. … 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 … grayslake sanitary districtNettetpolycyclic 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. choko heated gloves review

"NettetTHE 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. " - Linear codes over finite chain rings

Linear codes over finite chain rings

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

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 … 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 〈 …

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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. 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

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 ... 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 …

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 … 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 …

Nettet1. feb. 2024 · This Gray map establishes a bridge between the linear codes over finite chain rings and codes (could be non-linear) over finite fields. Our work is particularly …

NettetLinear Codes over the Finite Ring Z 15 ... In this paper, the structure of the non-chain ring Z 15 is studied. The ideals of the ring Z 15 are obtained through its non-units and the Lee weights of ele-ments in Z 15 are presented. On this basis, by the Chinese emainder R Theo-rem, we construct a unique expression of an element in Z chokolatta beverly hillsNettet29. 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 … grayslake roofing contractorNettet14. 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 ... chokolademousse madbandittenNettet1. 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 … grayslake rehabilitation centerNettet10. 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 ... chokolademousse med appelsinNettet1. 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. chokolatta north hollywood hillsNettet1. 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 ... chokolademousse med havtorn