2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | M.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. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
