Maximally Recoverable Local Repairable Codes From Subspace Direct Sum Systems

Shu Liu; Chaoping Xing

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Maximally Recoverable Local Repairable Codes From Subspace Direct Sum Systems

机译：Maximally Recoverable Local Repairable Codes From Subspace Direct Sum Systems

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Maximally recoverable local repairable codes (MR LRCs for short) have received great attention in the last few years. Various constructions have been proposed in literature. The main focus of this topic is to construct MR LRCs over small fields. An interesting parameter regime for an $(N=nr,r,h, delta)$ -MR LRC is the constant global parities $h=O(1)$ . In this parameter setting, all previous constructions require the field size $ell =Omega _{h} (N^{h-1-o(1)})$ . It remains challenging to improve this bound. In this paper, via subspace direct sum systems, we present a construction of MR LRC with the field size $ell = Oleft({N^{h-2+frac {1}{h-1}-o(1)}}right)$ . In particular, for the interesting cases where $h=2,3$ , we improve previous constructions by either reducing field size or removing constraints. In addition, we also offer some constructions of MR LRCs for larger global parity $h$ . The main techniques used in this paper is through subspace direct sum systems that we introduce.

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《IEEE Transactions on Information Theory》 |2023年第4期|2300-2310|共11页
作者
Shu Liu; Chaoping Xing;
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作者单位

National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, China|State Key Laboratory of Cryptology, Beijing, China;

School of Electronic Information and Electric Engineering, Shanghai Jiao Tong University, Shanghai, China;

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正文语种英语
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关键词
Codes; Servers; Upper bound; Computer crashes; Matrices; Distributed databases; Terminology;

Maximally Recoverable Local Repairable Codes From Subspace Direct Sum Systems

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