Constructions and Some Search Results of Ternary LRCs with d = 6

Youliang ZHENG  Ruihu LI  Jingjie LV  Qiang FU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E104-A   No.3   pp.644-649
Publication Date: 2021/03/01
Publicized: 2020/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2020EAL2070
Type of Manuscript: LETTER
Category: Coding Theory
locally repairable codes,  parity-check matrix,  disjoint repair groups,  

Full Text: FreePDF(180.8KB)

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.