Related papers: Explicit Maximally Recoverable Codes with Locality
When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…
We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms…
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 $t$…
In this paper, we propose several constructions of Locally Recoverable Codes from elliptic surfaces. In particular, we are able to obtain codes with availability $t>2$, codes with hierarchical locality and, finally, codes which combine…
We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic…
We introduce alphabet-permutation (AP) codes, a new family of error-correcting codes defined by iteratively applying random coordinate-wise permutations to a fixed initial word. A special case recovers random additive codes and random…
Locality enables storage systems to recover failed nodes from small subsets of surviving nodes. The setting where nodes are partitioned into subsets, each allowing for local recovery, is well understood. In this work we consider a…
In this letter, locally recoverable codes with maximal recoverability are studied with a focus on identifying the MDS codes resulting from puncturing and shortening. By using matroid theory and the relation between MDS codes and uniform…
In recent years, the rapidly increasing amounts of data created and processed through the internet resulted in distributed storage systems employing erasure coding based schemes. Aiming to balance the tradeoff between data recovery for…
We consider the locally repairable codes (LRC), aiming at sequential recovering multiple erasures. We define the (n,k,r,t)-SLRC (Sequential Locally Repairable Codes) as an [n,k] linear code where any t'(>= t) erasures can be sequentially…
In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements,…
A locally recoverable (LRC) code is a code over a finite field $\mathbb{F}_q$ such that any erased coordinate of a codeword can be recovered from a small number of other coordinates in that codeword. We construct LRC codes correcting more…
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…
Locally recoverable codes were introduced by Gopalan et al. in 2012, and in the same year Prakash et al. introduced the concept of codes with locality, which are a type of locally recoverable codes. In this work we introduce a new family of…
The focus of this paper is on linear, binary codes with locality having locality parameter $r$, that are capable of recovering from $t\geq 2$ erasures and that moreover, have short block length. Both sequential and parallel (through…
This paper develops a new family of locally recoverable codes for distributed storage systems, Sequential Locally Recoverable Codes (SLRCs) constructed to handle multiple erasures in a sequential recovery approach. We propose a new…
A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most $r$) other symbols of the codeword. In this paper we introduce a construction of LRC codes on…
We prove several results on linear codes achieving list-recovery capacity. We show that random linear codes achieve list-recovery capacity with constant output list size (independent of the alphabet size and length). That is, over alphabets…
A locally recoverable code (LRC code) is a code over a finite alphabet such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. In this paper we derive new finite-length and…
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…