Some Improvements on Locally Repairable Codes
Abstract
The locally repairable codes (LRCs) were introduced to correct erasures efficiently in distributed storage systems. LRCs are extensively studied recently. In this paper, we first deal with the open case remained in \cite{q} and derive an improved upper bound for the minimum distances of LRCs. We also give an explicit construction for LRCs attaining this bound. Secondly, we consider the constructions of LRCs with any locality and availability which have high code rate and minimum distance as large as possible. We give a graphical model for LRCs. By using the deep results from graph theory, we construct a family of LRCs with any locality and availability with code rate and optimal minimum distance where is the length of the code.
Cite
@article{arxiv.1506.04822,
title = {Some Improvements on Locally Repairable Codes},
author = {Jun Zhang and Xin Wang and Gennian Ge},
journal= {arXiv preprint arXiv:1506.04822},
year = {2015}
}
Comments
14 pages. arXiv admin note: text overlap with arXiv:1409.0952, arXiv:1311.3284 by other authors