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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

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 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 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 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 code) if every symbol in the encoding is a function of a small number (at most r) other symbols. A family of linear LRC codes that generalize the classic construction of…

Information Theory · Computer Science 2015-05-12 Alexander Barg , Itzhak Tamo , Serge Vladut

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

In a {\em locally recoverable} or {\em repairable} code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed…

Information Theory · Computer Science 2016-11-17 Viveck Cadambe , Arya Mazumdar

In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the…

Information Theory · Computer Science 2016-09-08 Toni Ernvall , Thomas Westerbäck , Camilla Hollanti , Ragnar Freij

Codes with locality, also known as locally recoverable codes, allow for recovery of erasures using proper subsets of other coordinates. These subsets are typically of small cardinality to promote recovery using limited network traffic and…

Information Theory · Computer Science 2025-01-23 Kathryn Haymaker , Beth Malmskog , Gretchen L. Matthews

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

We construct a family of linear maximally recoverable codes with locality $r$ and dimension $r+1.$ For codes of length $n$ with $r\approx n^\alpha, 0\le\alpha\le 1$ the code alphabet is of the order $n^{1+3\alpha},$ which improves upon the…

Information Theory · Computer Science 2023-03-07 Alexander Barg , Zitan Chen , Itzhak Tamo

In this paper, we propose several constructions of Locally Recoverable Codes from elliptic surfaces. In particular, we are able to obtain codes with availability $t>2$, codes with hierarchical locality and, finally, codes which combine…

Information Theory · Computer Science 2026-05-28 Elena Berardini , Andrea Fornetto

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

In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position $P$ of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $R_P$. The codes in the class…

Information Theory · Computer Science 2021-07-29 Cícero Carvalho , Victor G. L. Neumann

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

Locally recoverable codes are widely used in distributed and cloud storage systems. The objective of this paper is to present a construction of near MDS codes with oval polynomials and then determine the locality of the codes. It turns out…

Information Theory · Computer Science 2022-04-27 Xiaoru Li , Ziling Heng

A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we have $\delta$ non overlapping subsets of cardinality $r_i$ that…

Algebraic Geometry · Mathematics 2020-01-27 Daniele Bartoli , Maria Montanucci , Luciane Quoos
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