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In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it repair bandwidth} required to exactly regenerate a storage node after a failure arises. This repair bandwidth depends on the structure of the…
We consider the design of regenerating codes for distributed storage systems at the minimum bandwidth regeneration (MBR) point. The codes allow for a repair process that is exact and uncoded, but table-based. These codes were introduced in…
Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory…
Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems. This paper investigates a generalization of the usual locally…
Locally repairable codes enables fast repair of node failure in a distributed storage system. The code symbols in a codeword are stored in different storage nodes, such that a disk failure can be recovered by accessing a small fraction of…
In recent years, several classes of codes are introduced to provide some fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) play an important role. However,…
Recently, the research on local repair codes is mainly confined to repair the failed nodes within each repair group. But if the extreme cases occur that the entire repair group has failed, the local code stored in the failed group need to…
The locally repairable codes (LRCs) were introduced to correct erasures efficiently in distributed storage systems. LRCs are extensively studied recently. In this paper, we first deal with the open case remained in \cite{q} and derive an…
A locally repairable code with availability has the property that every code symbol can be recovered from multiple, disjoint subsets of other symbols of small size. In particular, a code symbol is said to have $(r,t)$-availability if it can…
We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same parameters, it produces…
Constructions of optimal locally repairable codes (LRCs) in the case of $(r+1) \nmid n$ and over small finite fields were stated as open problems for LRCs in [I. Tamo \emph{et al.}, "Optimal locally repairable codes and connections to…
Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than…
Data storage applications require erasure-correcting codes with prescribed sets of dependencies between data symbols and redundant symbols. The most common arrangement is to have $k$ data symbols and $h$ redundant symbols (that each depends…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these…
Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…
In recent years, locally repairable codes (LRCs) have attracted considerable attention owing to their pivotal role in distributed storage systems. Since binary linear locally repairable codes can significantly reduce the complexity of both…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
The decomposition theory of matroids initiated by Paul Seymour in the 1980's has had an enormous impact on research in matroid theory. This theory, when applied to matrices over the binary field, yields a powerful decomposition theory for…
This paper studies the design of codes for distributed storage systems (DSS) that enable local repair in the event of node failure. This paper presents locally repairable codes based on low degree multivariate polynomials. Its code…
Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…