Related papers: Optimal and Almost Optimal Locally Repairable Code…
Locally repairable codes have been extensively investigated due to practical applications in distributed and cloud storage systems in recent years. However, not much work on asymptotic behavior of locally repairable codes has been done. In…
We introduce a family of balanced locally repairable codes (BLRCs) $[n, k, d]$ for arbitrary values of $n$, $k$ and $d$. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low…
Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node,…
In this paper, a link between polymatroid theory and locally repairable codes (LRCs) is established. The codes considered here are completely general in that they are subsets of $A^n$, where $A$ is an arbitrary finite set. Three classes of…
Locally repairable codes (LRCs) have gained significant interest for the design of large distributed storage systems as they allow a small number of erased nodes to be recovered by accessing only a few others. Several works have thus been…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
In this work, we give locally repairable regenerating code (LRRC) [1]-[3], [5], [6] constructions that can protect the file size promised by the graph analysis of the modified family helper selection (MFHS) scheme [1] at the…
This thesis makes several significant contributions to the theory of both Regenerating (RG) and Locally Recoverable (LR) codes. The two principal contributions are characterizing the optimal rate of an LR code designed to recover from $t$…
We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the…
In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the…
In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error-correction capabilities. The corresponding decoding radius…
We consider the complexities of repair algorithms for locally repairable codes and propose a class of codes that repair single node failures using addition operations only, or codes with addition based repair. We construct two families of…
Locally Repairable Codes (LRC's) based on generalised quadrangles were introduced by Pamies-Juarez, Hollmann and Oggier in \cite{PaHoOg2013}, and bounds on the repairability and availability were derived. In this paper, we determine the…
In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…
We present a general framework for constructing high rate error correcting codes that are locally correctable (and hence locally decodable if linear) with a sublinear number of queries, based on lifting codes with respect to functions on…
Locally recoverable codes are error correcting codes with the additional property that every symbol of any codeword can be recovered from a small set of other symbols. This property is particularly desirable in cloud storage applications. A…
We introduce two new classes of covering codes in graphs for every positive integer $r$. These new codes are called local $r$-identifying and local $r$-locating-dominating codes and they are derived from $r$-identifying and…
A long standing problem has been to develop "good" binary linear codes to be used for error-correction. This paper investigates in some detail an attack on this problem using a connection between quadratic residue codes and hyperelliptic…
Recently, locally repairable codes has gained significant interest for their potential applications in distributed storage systems. However, most constructions in existence are over fields with size that grows with the number of servers,…
Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative the open question whether there exists a…