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Typically, locally repairable codes (LRCs) and regenerating codes have been studied independently of each other, and it has not been clear how the parameters of one relate to those of the other. In this paper, a novel connection between…

Information Theory · Computer Science 2016-11-22 Toni Ernvall , Thomas Westerbäck , Ragnar Freij-Hollanti , Camilla Hollanti

We prove that a class of distance-optimal local reconstruction codes (LRCs), an important family of repair-efficient codes for distributed storage systems, achieve the maximum distance separable private information retrieval capacity for…

Information Theory · Computer Science 2018-09-19 Siddhartha Kumar , Hsuan-Yin Lin , Eirik Rosnes , Alexandre Graell i Amat

Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…

Information Theory · Computer Science 2014-05-06 Dimitris S. Papailiopoulos , Alexandros G. Dimakis

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

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

In distributed storage systems, locally repairable codes (LRCs) are introduced to realize low disk I/O and repair cost. In order to tolerate multiple node failures, the LRCs with \emph{$(r, \delta)$-locality} are further proposed. Since hot…

Information Theory · Computer Science 2017-05-03 Bin Chen , Shu-Tao Xia , Jie Hao

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…

Information Theory · Computer Science 2025-03-05 Akram Baghban , Mehdi Ghiyasvand

Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…

Information Theory · Computer Science 2015-06-08 Steven T. Dougherty , Jon-Lark Kim , Buket Ozkaya , Lin Sok , Patrick Solé

Locally repairable codes (LRCs) are ingeniously designed distributed storage codes with a (usually small) fixed set of helper nodes participating in repair. Since most existing LRCs assume exact repair and allow full exchange of the stored…

Information Theory · Computer Science 2016-05-06 Imad Ahmad , Chih-Chun Wang

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…

Information Theory · Computer Science 2017-06-01 Stanislav Kruglik , Marina Dudina , Valeriya Potapova , Alexey Frolov

Linear complementary dual (LCD) cyclic codes were referred historically to as reversible cyclic codes, which had applications in data storage. Due to a newly discovered application in cryptography, there has been renewed interest in LCD…

Information Theory · Computer Science 2017-09-12 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

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

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

Motivated by applications in distributed storage, the notion of a locally recoverable code (LRC) was introduced a few years back. In an LRC, any coordinate of a codeword is recoverable by accessing only a small number of other coordinates.…

Information Theory · Computer Science 2023-08-01 Arya Mazumdar

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…

Information Theory · Computer Science 2016-11-17 Alexander Barg , Itzhak Tamo , Serge Vladuts

Modern large-scale distributed storage systems use erasure codes to protect against node failures with low storage overhead. In practice, the failure rate and other factors of storage devices in the system may vary significantly over time,…

Information Theory · Computer Science 2023-08-15 Xiangliang Kong

Locally repairable codes(LRCs) play important roles in distributed storage systems(DSS). LRCs with small locality have their own advantages since fewer available symbols are needed in the recovery of erased symbols. In this paper, we prove…

Information Theory · Computer Science 2022-07-08 Yuan Gao , Siman Yang

In distributed storage systems, locally repairable codes (LRCs) are designed to reduce disk I/O and repair costs by enabling recovery of each code symbol from a small number of other symbols. To handle multiple node failures,…

Information Theory · Computer Science 2023-07-11 Jing Qiu , Fang-Wei Fu

Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…

Information Theory · Computer Science 2020-05-19 Ted Hurley

We establish a duality result between linear index coding and Locally Repairable Codes (LRCs). Specifically, we show that a natural extension of LRCs we call Generalized Locally Repairable Codes (GLCRs) are exactly dual to linear index…

Information Theory · Computer Science 2014-02-18 Karthikeyan Shanmugam , Alexandros G. Dimakis