Constructions and some search results of ternary LRCs with d = 6

Abstract

Locally repairable codes (LRCs) are a type of new erasure codes designed for modern distributed storage systems (DSSs). In order to obtain ternary LRCs of distance 6, firstly, we propose constructions with disjoint repair groups and construct several families of LRCs with 1 ≤ r ≤ 6, where codes with 3 ≤ r ≤ 6 are obtained through a search algorithm. Then, we propose a new method to extend the length of codes without changing the distance. By employing the methods such as expansion and deletion, we obtain more LRCs from a known LRC. The resulting LRCs are optimal or near optimal in terms of the Cadambe-Mazumdar (C-M) bound.