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A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery…

Information Theory · Computer Science 2019-07-12 Irene Marquez-Corbella , Edgar Martinez-Moro , Carlos Munuera

A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the encoding is a function of a small number (at most $r$) other symbols. We present a family of LRC codes that attain the maximum possible value of the…

Information Theory · Computer Science 2014-07-14 Itzhak Tamo , Alexander Barg

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…

Information Theory · Computer Science 2017-02-07 Stanislav Kruglik , Alexey Frolov

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…

Information Theory · Computer Science 2015-01-29 S. B. Balaji , P. Vijay Kumar

A code is called a locally repairable code (LRC) if any code symbol is a function of a small fraction of other code symbols. When a locally repairable code is employed in a distributed storage systems, an erased symbol can be recovered by…

Information Theory · Computer Science 2021-11-25 Wei Zhao , Kenneth W. Shum , Shenghao Yang

In this paper, we consider the convertible code with locally repairable property. We present an improved lower bound on access cost associated with $(r,\delta)$. Then, we provide a general construction of convertible codes with optimal…

Information Theory · Computer Science 2025-12-29 Songping Ge , Han Cai , Xiaohu Tang

Recently, the research on local repair codes is mainly confined to repair the failed nodes within each repair group. But if the extreme cases occur that the entire repair group has failed, the local code stored in the failed group need to…

Information Theory · Computer Science 2016-02-10 Jing Wang , Zhiyuan Yan , Hongmei Xie

Locally repairable codes (LRCs) are considered with equal or unequal localities, local distances and local field sizes. An explicit two-layer architecture with a sum-rank outer code is obtained, having disjoint local groups and achieving…

Information Theory · Computer Science 2019-04-25 Umberto Martínez-Peñas , Frank R. Kschischang

Recent years, several new types of codes were introduced to provide fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) have played an important role. A…

Information Theory · Computer Science 2022-06-14 Yuanxiao Xi , Xiangliang Kong , Gennian Ge

Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than…

Information Theory · Computer Science 2016-11-15 Lluis Pamies-Juarez , Henk D. L. Hollmann , Frédérique Oggier

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,…

Information Theory · Computer Science 2025-04-16 Margreta Kuijper , Julia Lieb , Diego Napp

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…

Information Theory · Computer Science 2016-07-29 Abhishek Agarwal , Arya Mazumdar

In this work codes with availability are constructed based on the cyclic \emph{locally repairable code} (LRC) construction by Tamo et al. and their extension to $(r,\rho)$-locality by Chen et al. The minimum distance of these codes is…

Information Theory · Computer Science 2019-04-05 Lukas Holzbaur , Ragnar Freij-Hollanti , Antonia Wachter-Zeh

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…

Information Theory · Computer Science 2019-04-09 Ali Tebbi , Terence H. Chan , Chi Wan Sung

In an $[n,k,d]$ linear code, a code symbol is said to have locality $r$ if it can be repaired by accessing at most $r$ other code symbols. For an $(n,k,r)$ \emph{locally repairable code} (LRC), the minimum distance satisfies the well-known…

Information Theory · Computer Science 2017-02-21 Jie Hao , Shu-Tao Xia , Bin Chen

We construct Locally Recoverable Codes (LRCs) with availability $2$ from a family of fibered surfaces. To obtain the locality and availability properties, and to estimate the minimum distance of the codes, we combine techniques coming from…

Algebraic Geometry · Mathematics 2025-12-10 Cecília Salgado , Lara Vicino

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…

Information Theory · Computer Science 2020-02-14 Katina Kralevska , Danilo Gligoroski , Harald Øverby

Locally repairable codes (LRCs), which can recover any symbol of a codeword by reading only a small number of other symbols, have been widely used in real-world distributed storage systems, such as Microsoft Azure Storage and Ceph Storage…

Information Theory · Computer Science 2023-10-17 Wenqin Zhang , Deng Tang , Chenhao Ying , Yuan Luo

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,…

Information Theory · Computer Science 2013-02-05 Govinda M. Kamath , N. Prakash , V. Lalitha , P. Vijay Kumar

This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems which possess all-symbols locality and maximal possible minimum distance, or equivalently, can tolerate the maximal number…

Information Theory · Computer Science 2013-01-29 Natalia Silberstein , Ankit Singh Rawat , O. Ozan Koyluoglu , Sriram Vishwanath