Related papers: Optimal Quaternary (r,delta)-Locally Repairable Co…
The repair bandwidth of a code is the minimum amount of data required to repair one or several failed nodes (erasures). For MDS codes, the repair bandwidth is bounded below by the so-called cut-set bound, and codes that meet this bound with…
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…
Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…
Locally recoverable codes deal with the task of reconstructing a lost symbol by relying on a portion of the remaining coordinates smaller than an information set. We consider the case of codes over finite chain rings, generalizing known…
Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes…
Consider a linear [n,k,d]_q code C. We say that that i-th coordinate of C has locality r, if the value at this coordinate can be recovered from accessing some other r coordinates of C. Data storage applications require codes with small…
This paper presents a construction for several families of optimal binary locally repairable codes (LRCs) with small locality (2 and 3). This construction is based on various anticodes. It provides binary LRCs which attain the…
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…
Maximum distance separable (MDS) codes are widely used in distributed storage systems as they provide optimal fault tolerance for a given amount of storage overhead. The seminal work of Dimakis~\emph{et al.} first established a lower bound…
We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the…
Determinant codes are a class of exact-repair regenerating codes for distributed storage systems with parameters (n, k = d, d). These codes cover the entire trade-off between per-node storage and repair-bandwidth. In an earlier work of the…
Fractional repetition (FR) codes are a class of regenerating codes for distributed storage systems with an exact (table-based) repair process that is also uncoded, i.e., upon failure, a node is regenerated by simply downloading packets from…
Storage codes are used to ensure reliable storage of data in distributed systems. Here we consider functional repair codes, where individual storage nodes that fail may be repaired efficiently and the ability to recover original data and to…
Classical $(r,\delta)$-locally recoverable codes are designed for avoiding loss of information in large scale distributed and cloud storage systems. We introduce the quantum counterpart of those codes by defining quantum…
Locally repairable codes have been investigated extensively in recent years due to practical applications in distributed and cloud storage systems. However, there are few asymptotical constructions of locally repairable codes in the…
In this survey, two related families of codes are discussed: batch codes and codes for private information retrieval. These two families can be viewed as natural generalizations of locally repairable codes, which were extensively studied in…
In modern practical data centers, storage nodes are usually organized into equally sized groups, which is called racks. The cost of cross-rack communication is much more expensive compared with the intra-rack communication cost. The codes…
In distributed storage systems reliability is achieved through redundancy stored at different nodes in the network. Then a data collector can reconstruct source information even though some nodes fail. To maintain reliability, an autonomous…
We extend the notion of locality from the Hamming metric to the rank and subspace metrics. Our main contribution is to construct a class of array codes with locality constraints in the rank metric. Our motivation for constructing such codes…
A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates. We show that any {\em zero-error} $2$-query locally correctable code…