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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…

Information Theory · Computer Science 2022-08-23 Han Cai , Moshe Schwartz

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

For a code $\code$, its $i$-th symbol is said to have locality $r$ if its value can be recovered by accessing some other $r$ symbols of $\code$. Locally repairable codes (LRCs) are the family of codes such that every symbol has locality…

Information Theory · Computer Science 2016-01-25 Swanand Kadhe , Alex Sprintson

We consider the problem of designing [n; k] linear codes for distributed storage systems (DSS) that satisfy the (r, t)-Local Repair Property, where any t'(<=t) simultaneously failed nodes can be locally repaired, each with locality r. The…

Information Theory · Computer Science 2015-07-30 Wentu Song , Chau Yuen

In distributed storage systems, erasure codes with locality $r$ is preferred because a coordinate can be recovered by accessing at most $r$ other coordinates which in turn greatly reduces the disk I/O complexity for small $r$. However, the…

Information Theory · Computer Science 2014-10-20 Anyu Wang , Zhifang Zhang

Locally repairable codes enables fast repair of node failure in a distributed storage system. The code symbols in a codeword are stored in different storage nodes, such that a disk failure can be recovered by accessing a small fraction of…

Information Theory · Computer Science 2021-12-13 Kenneth W. Shum , Jie Hao

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

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

Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…

Information Theory · Computer Science 2016-09-29 Sreechakra Goparaju , Robert Calderbank

Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…

Information Theory · Computer Science 2020-11-09 Charul Rajput , Maheshanand Bhaintwal , Ramakrishna Bandi

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 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

In this paper, we propose locally repairable codes (LRCs) with optimal minimum distance for distributed storage systems (DSS). A two-layer encoding structure is employed to ensure data reconstruction and the designated repair locality. The…

Information Theory · Computer Science 2014-08-15 Hongmei Xie , Zhiyuan Yan

Local Reconstruction Codes (LRCs) allow for recovery from a small number of erasures in a local manner based on just a few other codeword symbols. A maximally recoverable (MR) LRC offers the best possible blend of such local and global…

Information Theory · Computer Science 2018-08-15 Venkatesan Guruswami , Lingfei Jin , Chaoping Xing

We study monomial-Cartesian codes (MCCs) which can be regarded as $(r,\delta)$-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to $(r,\delta)$-optimal…

Information Theory · Computer Science 2024-10-25 Carlos Galindo , Fernando Hernando , Helena Martín-Cruz

Locally repairable codes (LRCs) have attracted a lot of attention due to their applications in distributed storage systems. In this paper, we provide new constructions of optimal $(2, \delta)$-LRCs over $\mathbb{F}_q$ with flexible…

Information Theory · Computer Science 2024-10-07 Yuan Gao , Weijun Fang , Jingke Xu , Dong Wang , Sihuang Hu

Locally Repairable Codes (LRC's) based on generalised quadrangles were introduced by Pamies-Juarez, Hollmann and Oggier in \cite{PaHoOg2013}, and bounds on the repairability and availability were derived. In this paper, we determine the…

Combinatorics · Mathematics 2019-12-16 Michel Lavrauw , Geertrui Van de Voorde

Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory…

Information Theory · Computer Science 2021-02-02 Pan Tan , Cuiling Fan , Cunsheng Ding , Zhengchun Zhou

A code is said to be a Locally Recoverable Code (LRC) with availability if every coordinate can be recovered from multiple disjoint sets of other coordinates called recovering sets. The vector of sizes of recovering sets of a coordinate is…

Information Theory · Computer Science 2017-05-16 Sourbh Bhadane , Andrew Thangaraj

We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…

Combinatorics · Mathematics 2024-06-25 Aida Abiad , Alexander L. Gavrilyuk , Antonina P. Khramova , Ilia Ponomarenko