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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

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

A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. Building on work of Barg, Tamo, and…

Information Theory · Computer Science 2020-01-16 Alexander Barg , Kathryn Haymaker , Everett W. Howe , Gretchen L. Matthews , Anthony Várilly-Alvarado

Locally recoverable (LRC) codes provide ways of recovering erased coordinates of the codeword without having to access each of the remaining coordinates. A subfamily of LRC codes with hierarchical locality (H-LRC codes) provides added…

Information Theory · Computer Science 2019-04-03 Sean Ballentine , Alexander Barg , Serge Vladuts

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…

Information Theory · Computer Science 2014-02-06 Itzhak Tamo , Alexander Barg

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. In this paper we derive new finite-length and…

Information Theory · Computer Science 2016-03-10 Itzhak Tamo , Alexander Barg , Alexey Frolov

We study the locally recoverable codes on algebraic curves. In the first part of this article, we provide a bound of generalized Hamming weight of these codes. Whereas in the second part, we propose a new family of algebraic geometric LRC…

Commutative Algebra · Mathematics 2016-05-25 Edoardo Ballico , Chiara Marcolla

A linear error correcting code is a subspace of a finite-dimensional space over a finite field with a fixed coordinate system. Such a code is said to be locally recoverable with locality $r$ if, for every coordinate, its value at a codeword…

Information Theory · Computer Science 2021-02-22 Cecília Salgado , Anthony Várilly-Alvarado , José Felipe Voloch

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. We study Locally Recoverable Algebraic Geometry codes arising from…

Information Theory · Computer Science 2018-06-08 Carlos Munuera , Wanderson Tenório , Fernando Torres

A code is locally recoverable when each symbol in one of its code words can be reconstructed as a function of $r$ other symbols. We use bundles of projective spaces over a line to construct locally recoverable codes with availability; that…

In this paper, we present a construction of locally recoverable codes (LRCs) with multiple recovery sets using algebraic curves with many rational points. By leveraging separable morphisms between smooth projective curves and expanding the…

Algebraic Geometry · Mathematics 2025-09-19 Saeed Tafazolian , Jaa Top

In this paper, we introduce curve-lifted codes over fields of arbitrary characteristic, inspired by Hermitian-lifted codes over $\mathbb{F}_{2^r}$. These codes are designed for locality and availability, and their particular parameters…

Information Theory · Computer Science 2023-07-26 Gretchen L. Matthews , Travis Morrison , Aidan W. Murphy

A locally recoverable code is an error-correcting code such that any erasure in a coordinate of a codeword can be recovered from a set of other few coordinates. In this article we introduce a model of local recoverable codes that also…

Information Theory · Computer Science 2018-12-04 Carlos Munuera

A locally recoverable (LRC) code is a code over a finite field $\mathbb{F}_q$ such that any erased coordinate of a codeword can be recovered from a small number of other coordinates in that codeword. We construct LRC codes correcting more…

Information Theory · Computer Science 2024-05-01 Carlos Galindo , Fernando Hernando , Carlos Munuera

We generalize the construction of locally recoverable codes on algebraic curves given by Barg, Tamo and Vl\u{a}du\c{t} to those with arbitrarily many recovery sets by exploiting the structure of fiber products of curves. Employing maximal…

Number Theory · Mathematics 2018-08-17 Kathryn Haymaker , Beth Malmskog , Gretchen Matthews

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

By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local…

Information Theory · Computer Science 2018-12-07 S. B. Balaji , Ganesh R. Kini , P. Vijay Kumar

Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…

Information Theory · Computer Science 2018-05-16 Abhishek Agarwal , Alexander Barg , Sihuang Hu , Arya Mazumdar , Itzhak Tamo

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

Locally recoverable codes deal with the task of reconstructing a lost symbol by relying on a portion of the remaining coordinates smaller than an information set. We consider the case of codes over finite chain rings, generalizing known…

Information Theory · Computer Science 2024-01-11 Giulia Cavicchioni , Eleonora Guerrini , Alessio Meneghetti
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