Optimal locally repairable codes via rank-metric codes

Abstract

This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems which possess all-symbol locality and the largest possible minimum distance, or equivalently, can tolerate the maximum number of node failures. This construction, based on maximum rank distance (MRD) Gabidulin codes, provides new optimal vector and scalar LRCs. In addition, the paper also discusses mechanisms by which codes obtained using this construction can be used to construct LRCs with efficient local repair of failed nodes by combination of LRCs with regenerating codes.