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Related papers: Cyclic and convolutional codes with locality

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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

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

Information Theory · Computer Science 2017-02-10 Itzhak Tamo , Alexander Barg , Sreechakra Goparaju , Robert Calderbank

A locally recoverable code of locality $r$ over $\mathbb{F}_{q}$ is a code where every coordinate of a codeword can be recovered using the values of at most $r$ other coordinates of that codeword. Locally recoverable codes are efficient at…

Information Theory · Computer Science 2024-06-19 Gustavo Terra Bastos , Angelynn Alvarez , Zachary Flores , Adriana Salerno

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

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

Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have…

Information Theory · Computer Science 2023-03-14 Weijun Fang , Fang-Wei Fu , Bin Chen , Shu-Tao Xia

Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do…

Information Theory · Computer Science 2015-11-24 Pengfei Huang , Eitan Yaakobi , Hironori Uchikawa , Paul H. Siegel

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

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

In this work the construction of LRC codes given in [6] is completed, in the case of even characteristic. A general construction is presented, that enables us to obtain linear LRC codes of large length $n \approx q^4$, dimension and…

Information Theory · Computer Science 2026-04-07 Francisco Galluccio

Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…

Information Theory · Computer Science 2021-05-10 D. Shivakrishna , Aaditya M. Nair , V. Lalitha

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

Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…

Information Theory · Computer Science 2019-04-09 Aaditya M Nair , V. Lalitha

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 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

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 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

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

This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in…

Information Theory · Computer Science 2010-12-16 Qin Huang , Qiuju Diao , Shu Lin , Khaled Abdel-Ghaffar

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
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