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 … http://maths.ccnu.edu.cn/info/1045/28050.htm

Hermitian duality of left dihedral codes over finite fields

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 … 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 ... kristal dias county commissioner

Linear codes over finite rings are trace codes - ScienceDirect

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 … 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. map north arrow symbol

ON POLYCYCLIC CODES OVER A FINITE CHAIN RING - arXiv

Linear complementary pairs of codes over rings SpringerLink

Nettet1. okt. 2024 · Codes over finite commutative rings have been studied for almost 50 years. The main motivation of studying codes over rings is that they can be associated with codes over finite fields through the Gray map. Recently, most of studies concentrated on codes over finite non-chain ring. Nettet1. des. 2024 · Linear codes over finite rings also have a lot of outstanding and remarkable applications, and have been studied since Hammons et al. found significant classes of Z 4 -codes such as the Kerdock, Preparata, Goethals codes and so on [11]. For more details of codes over finite rings, see [23]. map north and south koreaNettetCodes 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 . krista lee clothing

"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 … " - Linear codes over finite chain rings

Linear codes over finite chain rings

On homogeneous arcs and linear codes over finite chain …

http://www.kurims.kyoto-u.ac.jp/EMIS/journals/EJC/Volume_7/PDF/v7i1r11.pdf Nettet7. aug. 2024 · We design a decoding algorithm for linear codes over finite chain rings given by their parity check matrices. It is assumed that decoding algorithms over the residue field are known at each degree of the adic decomposition. Keywords: chain ring; linear code; decoding; parity check matrix 1. Introduction

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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 … 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 …

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 ... 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.

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 Nettet1. jan. 2000 · Request PDF Linear Codes over Finite Chain Rings The aim of this paper is to develop a theory of linear codes over nite chain rings from a geometric viewpoint.

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 …

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 kristal cry baby dollNettet11. 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 … map north andoverNettetthe theory of linear codes over nite chain rings from a geometric viewpoint. Moreover, Norton studied the structure of linear codes over nite chain rings and generalized … map north and central americaNettet17. 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 . map north atlantic countriesNettet4. 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... map north america indian pyramidsNettet1. 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 … map north africa countriesNettet1. 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) map north africa and mediterranean