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Related papers: On cyclic LRC codes that are also LCD codes

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We consider the locally repairable codes (LRC), aiming at sequential recovering multiple erasures. We define the (n,k,r,t)-SLRC (Sequential Locally Repairable Codes) as an [n,k] linear code where any t'(>= t) erasures can be sequentially…

Information Theory · Computer Science 2016-11-01 Wentu Song , Kai Cai , Chau Yuen

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

Locally recoverable codes (LRCs) are classical error-correcting codes widely used in large scale distributed and cloud storage systems. Quantum locally recoverable codes (quantum LRCs) are the quantum counterpart of classical LRCs. They…

Information Theory · Computer Science 2025-08-06 Carlos Galindo , Fernando Hernando , Carlos Munuera , Diego Ruano

LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are…

Information Theory · Computer Science 2016-08-08 Cem Güneri , Buket Özkaya , Patrick Solé

Locally repairable codes (LRCs) have recently been widely used in distributed storage systems and the LRCs with $(r,\delta)$-locality ($(r,\delta)$-LRCs) attracted a lot of interest for tolerating multiple erasures. Ge et al. constructed…

Information Theory · Computer Science 2023-04-28 Yaxin Wang , Siman Yang

Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have very recently been introduced for their potential…

Information Theory · Computer Science 2023-12-19 Gaojun Luo , Bocong Chen , Martianus Frederic Ezerman , San Ling

Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, $ \partial - 1 $ erasures per local group), and…

Information Theory · Computer Science 2020-12-08 Umberto Martínez-Peñas , Diego Napp

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

Distributed and cloud storage systems are used to reliably store large-scale data. Erasure codes have been recently proposed and used in real-world distributed and cloud storage systems such as Google File System, Microsoft Azure Storage,…

Information Theory · Computer Science 2017-09-08 Mehrtash Mehrabi , Massoud Ardakani

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

Recently, locally repairable codes (LRCs) with local erasure correction constraints that are unequal and disjoint have been proposed. In this work, we study the same topic and provide some improved and additional results.

Information Theory · Computer Science 2017-04-10 Geonu Kim , Jungwoo Lee

Recent studies have delved into the construction of locally repairable codes (LRCs) with optimal minimum distance from function fields. In this paper, we present several novel constructions by extending the findings of optimally designed…

Information Theory · Computer Science 2025-02-03 Yunlong Zhu , Chang-An Zhao

Recent years, several new types of codes were introduced to provide fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) have played an important role. A…

Information Theory · Computer Science 2022-06-14 Yuanxiao Xi , Xiangliang Kong , Gennian Ge

Recently, Linear Complementary Dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and…

Information Theory · Computer Science 2024-09-13 Yansheng Wu , Jin Ma , Shandong Yang

We introduce a family of balanced locally repairable codes (BLRCs) $[n, k, d]$ for arbitrary values of $n$, $k$ and $d$. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low…

Information Theory · Computer Science 2020-02-14 Katina Kralevska , Danilo Gligoroski , Harald Øverby

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

Erasure codes play an important role in storage systems to prevent data loss. In this work, we study a class of erasure codes called Multi-Erasure Locally Recoverable Codes (ME-LRCs) for storage arrays. Compared to previous related works,…

Information Theory · Computer Science 2017-09-29 Pengfei Huang , Eitan Yaakobi , Paul H. Siegel

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 this work, we introduce maximally recoverable codes with locality and availability. We consider locally repairable codes (LRCs) where certain subsets of $ t $ symbols belong each to $ N $ local repair sets, which are pairwise disjoint…

Information Theory · Computer Science 2026-05-18 Umberto Martínez-Peñas , V. Lalitha

In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error-correction capabilities. The corresponding decoding radius…

Information Theory · Computer Science 2020-09-16 Lukas Holzbaur , Sven Puchinger , Antonia Wachter-Zeh