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Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…

Information Theory · Computer Science 2016-05-24 Antti Pöllänen , Thomas Westerbäck , Ragnar Freij-Hollanti , Camilla Hollanti

Petabyte-scale distributed storage systems are currently transitioning to erasure codes to achieve higher storage efficiency. Classical codes like Reed-Solomon are highly sub-optimal for distributed environments due to their high overhead…

Information Theory · Computer Science 2013-11-07 Itzhak Tamo , Dimitris S. Papailiopoulos , Alexandros G. Dimakis

Locally recoverable codes (LRCs) with locality parameter $r$ can recover any erased code symbol by accessing $r$ other code symbols. This local recovery property is of great interest in large-scale distributed classical data storage systems…

Information Theory · Computer Science 2024-11-05 Sandeep Sharma , Vinayak Ramkumar , Itzhak Tamo

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

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

Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, we first build a bridge between locally repairable code and packing. As an application of this bridge, some optimal…

Information Theory · Computer Science 2016-07-07 Han Cai , Minquan Cheng , Cuiling Fan , Xiaohu Tang

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…

Information Theory · Computer Science 2014-09-04 Anyu Wang , Zhifang Zhang

The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these…

Information Theory · Computer Science 2018-11-19 Sivakanth Gopi , Venkatesan Guruswami , Sergey Yekhanin

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

Cyclic codes are an important class of linear codes. Bounding the minimum distance of cyclic codes is a long-standing research topic in coding theory, and several well-known and basic results have been developed on this topic. Recently,…

Information Theory · Computer Science 2023-10-12 Jing Qiu , Weijun Fang , Fang-Wei Fu

Optimal locally repairable codes with information locality are considered. Optimal codes are constructed, whose length is also order-optimal with respect to a new bound on the code length derived in this paper. The length of the constructed…

Information Theory · Computer Science 2020-02-07 Han Cai , Moshe Schwartz

In this paper, codes with locality for four erasures are considered. An upper bound on the rate of codes with locality with sequential recovery from four erasures is derived. The rate bound derived here is field independent. An optimal…

Information Theory · Computer Science 2016-11-04 S. B. Balaji , K. P. Prasanth , P. Vijay Kumar

In this paper, we present new constructions of $q$-ary Singleton-optimal locally repairable codes (LRCs) with minimum distance $d=6$ and locality $r=3$, based on combinatorial structures from finite geometry. By exploiting the well-known…

Information Theory · Computer Science 2026-02-26 Yanzhen Xiong , Jianbing Lu

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

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

A locally repairable code with availability has the property that every code symbol can be recovered from multiple, disjoint subsets of other symbols of small size. In particular, a code symbol is said to have $(r,t)$-availability if it can…

Information Theory · Computer Science 2017-09-15 Swanand Kadhe , Robert Calderbank

We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and…

Information Theory · Computer Science 2015-02-06 Itzhak Tamo , Alexander Barg , Sreechakra Goparaju , Robert Calderbank

Constructing locally repairable codes achieving Singleton-type bound (we call them optimal codes in this paper) is a challenging task and has attracted great attention in the last few years. Tamo and Barg \cite{TB14} first gave a…

Information Theory · Computer Science 2017-12-14 Xudong Li , Liming Ma , Chaoping Xing

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…

Information Theory · Computer Science 2017-01-25 Mostafa Shahabinejad , Majid Khabbazian , Masoud Ardakani