2020/12/30 by Xiangliang Kong, Xin Wang, Kong, Xiangliang +3 · 4 citations
Computer Science · #94B60 #Advanced Data Storage Technologies #Caching and Content Delivery #Cellular Automata and Applications #E.4 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2012.15094
openalex publication_date 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the research of LRCs, bounds and constructions of the corresponding optimal codes are of particular concerns. In this work, codes with (r,δ)-locality which have optimal minimal distance w.r.t. the bound given by Prakash et al. \citePrakash2012Optimal are considered. Through parity check matrix approach, constructions of both optimal (r,δ)-LRCs with all symbol locality ((r,δ)a-LRCs) and optimal (r,δ)-LRCs with information locality ((r,δ)i-LRCs) are provided. As a generalization of a work of Xing and Yuan \citeXY19, these constructions are built on a connection between sparse hypergraphs and optimal (r,δ)-LRCs. With the help of constructions of large sparse hypergraphs, the length of codes constructed can be super-linear in the alphabet size. This improves upon previous constructions when the minimal distance of the code is at least 3δ+1. As two applications, optimal H-LRCs with super-linear length and GSD codes with unbounded length are also constructed.