Optimal locally repairable linear codes
WebOptimal linear codes with a local-error-correction property. N. Prakash, G. Kamath, V. Lalitha, P. V. Kumar; ... This paper uses matrix-product codes to propose two infinite families of q-ary optimal (r, δ) locally repairable codes of lengths up to q + q and construction of a third family, which has unbounded lengths not divisible by r + δ − 1. WebSep 1, 2024 · Like linear codes, -LRCs have a similar Singleton-like bound: (1) In particular, when , an -LRC degenerates to an r -LRC. In this paper, the optimal LRC means that the code reaches the Singleton-like bound. A great deal of research has been done on the construction of optimal LRCs.
Optimal locally repairable linear codes
Did you know?
WebJul 20, 2024 · A -ary ( ) locally repairable code (LRC) is an [ ] linear code where every code symbol can be repaired by accessing at most other code symbols. Its minimum distance satisfies the well-known Singleton-like bound. In this paper, we determine all the possible parameters of quaternary LRCs attaining this Singleton-like bound by employing a parity … WebJan 1, 2024 · The locality of a locally repairable code for a distributed storage system is the number of nodes that participate in the repair process, which characterizes the repair cost. In this paper, firstly, some LRCs with locality r = 2 generated by special matrices are proved, and some methods of constructing generator matrix are proposed. Next, we ...
WebOptimal Locally Repairable Linear Codes Wentu Song, Son Hoang Dau, Chau Yuen and Tiffany Jing Li Abstract—Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n,k,d] code having all-symbol(r,δ)-locality, denoted as(r,δ) a, is considered optimal if it also meets the minimum Hamming distance bound. WebJul 12, 2024 · Abstract: Optimal locally repairable codes with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve and generalize previously known bounds. Optimal codes are constructed, whose length is order optimal when compared with the …
WebApr 9, 2024 · In this paper, we propose infinite families of linear codes which are optimal or distance-optimal with respect to the Griesmer bound. Furthermore, we investigate the … WebMay 1, 2024 · Moreover, a necessary and sufficient condition for such linear codes to be Griesmer codes is presented. Secondly, as an application in data storage systems, we investigate the locality of the linear codes constructed. Furthermore, we show that these linear codes are alphabet-optimal locally repairable codes with locality 2.
WebDec 5, 2024 · Optimal LRC codes are those whose parameters achieve the generalized Singleton bound with equality. In the present paper, we are interested in studying optimal LRC codes over small fields and, more precisely, over $\mathbb{F}_4$. We shall adopt an approach by investigating optimal quaternary $(r,\delta)$-LRC codes through their parity …
Weblocality of the NMDS codes and obtain many families of distance-optimal and dimension-optimal locally repairable codes. Keywords: Linear code, near MDS code, locally recoverable codes 2000 MSC: 94B05, 94A05 1. Introduction Let q be a prime power and F q the finite field with q elements. Denote by F∗q =F q \{0}. bishop hartley football schedule 2021WebA Singleton-type bound for locally repairable codes relating its length n, dimension k, minimum distance d and locality r was first shown in the highly influential work [7]. It states that a linear locally repairable code C must obey1 d(C) 6n−k − ˘ k r ˇ +2. bishop hartley football live streamWebSep 1, 2024 · In distributed storage systems, locally repairable codes (LRCs) can effectively reduce the complexity of repairing failed nodes. In this paper, we constructed six classes … dark leather sofaWebDec 31, 2024 · Abstract Locally repairable codes which are optimal with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are... bishop hartley football schedule 2022WebDec 31, 2024 · Locally repairable codes which are optimal with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve and generalize previously known bounds. Optimal codes are constructed, whose length is order-optimal when compared with the … dark leather shoesWebIn particular, for locality r ∈ { 2, 3 } and minimum distance d = 6, we construct optimal binary linear LRCs with disjoint repair groups for almost all possible parameters. It should be … dark leather sectional sofaWebJul 20, 2024 · On Optimal Quaternary Locally Repairable Codes Abstract: A -ary ( ) locally repairable code (LRC) is an [ ] linear code where every code symbol can be repaired by … bishop hartley lunch