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Optimal constacyclic locally repairable codes
IEEE Communications Letters, 2019Being part of distributed storage systems, locally repairable codes (LRCs) have drawn great attention in the past years. Inspired by a recent construction of optimal LRCs-based on cyclic codes, constacyclic LRCs are studied in this letter. Specifically, a family of optimal constacyclic $(r,\delta)_{q}$ -LRCs with unbounded length and minimum ...
Zhonghua Sun, Shixin Zhu, Liqi Wang
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Locally Repairable Codes with Heterogeneous Locality Constraints
2018 IEEE Information Theory Workshop (ITW), 2018A code over a finite alphabet is called locally repairable codes (LRCs) if every symbol in the encoding is a function of a small number of other symbols of the codeword. In this paper, we study LRCs with heterogeneous locality constraints. We introduce $(n,\ k,\ r_{i},\ \delta_{i},\ i\ \in\ [m])$ LRCs which generalize the LRCs with equal $(r,\ \delta)$-
Qi Chen, Chunming Tang, Zhiqiang Lin
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On Optimal Quaternary Locally Repairable Codes
2021 IEEE International Symposium on Information Theory (ISIT), 2021A $q$ -ary ( $n, k, r$ ) locally repairable code (LRC) is an [ $n, k, d$ ] linear code where every code symbol can be repaired by accessing at most $r$ other code symbols. Its minimum distance satisfies the well-known Singleton-like bound. In this paper, we determine all the possible parameters of quaternary LRCs attaining this Singleton-like bound ...
Jie Hao +4 more
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Locally repairable codes with locality 1 and availability
2016 International Conference on Information and Communication Technology Convergence (ICTC), 2016In this paper, we propose an optimal scalar locally repairable code (LRC) with locality 1 in the sense of achieving the maximum possible minimum distance using the serial concatenation technique. A technique to construct an optimal vector LRC with locality 1 based on the proposed scalar LRC is also provided.
Mi-Young Nam +2 more
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Locally repairable codes from combinatorial designs
Science China Information Sciences, 2020Locally repairable codes (LRCs) were proposed to reduce the repair degree in distributed storage systems. In particular, LRCs with availability are highly desirable for distributed storage systems, since this kind of codes provide the mechanism of local repair for code symbols and parallel reading of hot data.
Yu Zhang, Haibin Kan
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Optimal ternary locally repairable codes
Designs, Codes and CryptographyFor a \([n, k, d]\) linear code \(\mathcal{C}\) over \(\mathbb{F}_q,\) a code symbol is said to have locality \(r\) if it can be repaired by accessing at most \(r\) other code symbols. The code \(\mathcal{C}\) is an \((n, k, r )\) locally repairable codes (LRC) if all the code symbols have locality \(r.\) An LRC is optimal if its minimum distance ...
Jie Hao +5 more
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Linear locally repairable codes with availability
2015 IEEE International Symposium on Information Theory (ISIT), 2015In this work, we present a new upper bound on the minimum distance d of linear locally repairable codes (LRCs) with information locality and availability. The bound takes into account the code length n, dimension k, locality r, availability t, and field size q. We use tensor product codes to construct several families of LRCs with information locality,
Pengfei Huang +3 more
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Cyclic linear binary locally repairable codes
2015 IEEE Information Theory Workshop (ITW), 2015Locally 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 not explicitly take into consideration the field size q, i.e., the size of the code alphabet.
Pengfei Huang +3 more
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