Related papers: New Constructions of Optimal Locally Repairable Co…
In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015codes} with an algebraic number theoretical approach that…
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…
Locally recoverable codes are widely used in distributed and cloud storage systems. The objective of this paper is to present a construction of near MDS codes with oval polynomials and then determine the locality of the codes. It turns out…
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…
In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs…
We propose locally rewritable codes (LWC) for resistive memories inspired by locally repairable codes (LRC) for distributed storage systems. Small values of repair locality of LRC enable fast repair of a single failed node since the lost…
New asymptotic upper bounds are presented on the rate of sequences of locally repairable codes (LRCs) with a prescribed relative minimum distance and locality over a finite field $F$. The bounds apply to LRCs in which the recovery functions…
The matrix completion problem provides a unifying lens through which many fundamental problems in coding theory can be viewed. In this paper, we investigate Locally Recoverable Codes (LRCs) with Maximal Recoverability (MR) and Maximum…
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. Bounds on the rate and distance of such codes have…
In a recent work, quantum locally recoverable codes (qLRCs) have been introduced for their potential application in large-scale quantum data storage and implication for quantum LDPC codes. This work focuses on the bounds and constructions…
This paper studies optimal quantum $(r,\delta)$-LRCs from matrix-product (MP) codes. We establish a necessary and sufficient condition for an MP code to be an optimal $(r,\delta)$-LRC. Based on this, we present a characterization for…
This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSS). Security and local-repairability are both important as features of an efficient storage system, and this paper…
By incorporating the concept of locality into quantum information theory, quantum locally recoverable codes (qLRCs) have been proposed, motivated by their potential applications in large-scale quantum data storage and their relevance to…
In this paper, we discuss codes for distributed storage systems with hierarchical repair properties. Specifically, we devote attention to the repair problem of the rack-aware storage model with locality, aiming to enhance the system's…
For binary $[n,k,d]$ linear locally repairable codes (LRCs), two new upper bounds on $k$ are derived. The first one applies to LRCs with disjoint local repair groups, for general values of $n,d$ and locality $r$, containing some previously…
We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable…
An [n, k] linear code C that is subject to locality constraints imposed by a parity check matrix H0 is said to be a maximally recoverable (MR) code if it can recover from any erasure pattern that some k-dimensional subcode of the null space…
A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we have $\delta$ non overlapping subsets of cardinality $r_i$ that…
Recently, locally repairable codes (LRCs) with local erasure correction constraints that are unequal and disjoint have been proposed. In this work, we study the same topic and provide some improved and additional results.
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…