Technical Program

Paper Detail

Paper IDM.3.1
Paper Title Perfect LRCs and k-Optimal LRCs
Authors Weijun Fang, Bin Chen, Shu-Tao Xia, Tsinghua University, China; Fang-Wei Fu, Nankai University, China
Session M.3: Codes for Distributed Storage III
Presentation Lecture
Track Coding for Storage and Memories
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract Linear codes with locality, called locally repairable codes (LRCs), have been applied in distributed storage systems (DSSs) to minimize the number of storage nodes to be downloaded during repairing a failed node. A linear code has locality $r$ if one can recover an erased code symbol by accessing at most $r$ other code symbols. Bounds and constructions of LRCs have been widely investigated in recent years. In this paper, we first propose the definition of perfect LRCs, whose dimension $k$ achieves the Hamming-type bound proposed by Wang \emph{et al.} (TIT2019). We establish important connections of the existence of LRCs with finite geometry and finite fields, then two systematic constructions of perfect LRCs are obtained. Rewriting the Hamming-type bound by the property of integers, we present a new construction of $k$-optimal LRCs achieving this bound, which have longer length than the previously known ones.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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