Optimal locally repairable codes with multiple repair sets based on 2-regular packings

Abstract

Locally repairable codes can improve the repair efficiency in distributed storage system. In this paper, we consider the locally repairable codes with multiple disjoint repair sets and each repair set contains exactly one check symbol. We obtain optimal locally repairable codes with $d=\delta =3$ by constructing 2-regular packings. Firstly, we present several 2-regular packings by using two special configurations. Then we apply these 2-regular packings to construct optimal ${[k+\lceil \frac{2k}{r}\rceil ,k,3]}_q$ systematic codes with information ${(r,3;1)}_c$-locality.