Related papers: Locally recoverable codes on surfaces
Locally repairable codes (LRC) have recently been a subject of intense research due to theoretical appeal and their application in distributed storage systems. In an LRC, any coordinate of a codeword can be recovered by accessing only few…
A locally recoverable code of locality $r$ over $\mathbb{F}_{q}$ is a code where every coordinate of a codeword can be recovered using the values of at most $r$ other coordinates of that codeword. Locally recoverable codes are efficient at…
A linear block code with dimension $k$, length $n$, and minimum distance $d$ is called a locally repairable code (LRC) with locality $r$ if it can retrieve any coded symbol by at most $r$ other coded symbols. LRCs have been recently…
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…
Employing underlying geometric and algebraic structures allows for constructing bespoke codes for local recovery of erasures. We survey techniques for enriching classical codes with additional machinery, such as using lines or curves in…
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…
By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local…
The locally repairable code (LRC) studied in this paper is an $[n,k]$ linear code of which the value at each coordinate can be recovered by a linear combination of at most $r$ other coordinates. The central problem in this work is to…
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…
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 (LRCs) are classical error-correcting codes widely used in large scale distributed and cloud storage systems. Quantum locally recoverable codes (quantum LRCs) are the quantum counterpart of classical LRCs. They…
Locally repairable codes, or locally recoverable codes (LRC for short) are designed for application in distributed and cloud storage systems. Similar to classical block codes, there is an important bound called the Singleton-type bound for…
A major issue of locally repairable codes is their robustness. If a local repair group is not able to perform the repair process, this will result in increasing the repair cost. Therefore, it is critical for a locally repairable code to…
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…
Classical locally recoverable codes, which permit highly efficient recovery from localized errors as well as global recovery from larger errors, provide some of the most useful codes for distributed data storage in practice. In this paper,…
We introduce the concept of quantum locally recoverable codes (qLRCs) with intersecting recovery sets. We derive a singleton-like bound for these codes by leveraging the additional information provided by the intersecting recovery sets.…
As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the…
We give a method to construct Locally Recoverable Error-Correcting codes. This method is based on the use of rational maps between affine spaces. The recovery of erasures is carried out by Lagrangian interpolation in general and simply by…
In this work, we introduce maximally recoverable codes with locality and availability. We consider locally repairable codes (LRCs) where certain subsets of $ t $ symbols belong each to $ N $ local repair sets, which are pairwise disjoint…
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…