Constructions of optimal binary locally repairable codes via intersection subspaces  

作　　者：Wenqin ZHANG Deng TANG Chenhao YING Yuan LUO 

机构地区：[1]School of Electronic Information and Electrical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China

出　　处：《Science China(Information Sciences)》2024年第6期414-428,共15页中国科学（信息科学）（英文版）

基　　金：supported in part by National Key R&D Program of China(Grant Nos.2022YFA1004900,2022YFA1005000);National Natural Science Foundation of China(Grant No.62272303)。

摘　　要：Locally repairable codes(LRCs),which can recover any symbol of a codeword by reading only a small number of other symbols,have been widely used in real-world distributed storage systems,such as Microsoft Azure Storage and Ceph Storage Cluster.Since binary linear LRCs can significantly reduce coding and decoding complexity,constructions of binary LRCs are of particular interest.The aim of this paper is to construct dimensional optimal binary LRCs with disjoint local repair groups.We introduce a method to connect intersection subspaces with binary LRCs and construct dimensional optimal binary linear LRCs with locality 2~b(b 3)and minimum distance d 6 by employing intersection subspaces deduced from the direct sum.This method will sufficiently increase the number of possible repair groups of dimensional optimal LRCs,thus efficiently expanding the range of the construction parameters while keeping the largest code rates compared with all known binary linear LRCs with minimum distance d 6 and locality 2~b.

关 键 词：locally repairable codes disjoint local repair groups distributed storage systems intersection subspaces direct sum 

分 类 号：TP333[自动化与计算机技术—计算机系统结构] TN911.22[自动化与计算机技术—计算机科学与技术]