Construction of Singleton-type optimal LRCs from existing LRCs and Near-MDS codes

摘要

Modern large scale distributed storage systems play a centralrole in data center and cloud storage, while node failure in data centeris common. The lost data in failure node must be recovered e ciently.Locally repairable codes (LRCs) are designed to solve this problem. Thelocality of an LRC is the number of nodes that participate in recovering thelost data from node failure, which characterizes the repair e ciency. AnLRC is called optimal if its minimum distance attains Singleton-type upperbound [1]. In this paper, using basic techniques of linear algebra over finitefield, infinite optimal LRCs over extension fields are derived from a givenoptimal LRC over base field(or small field). Next, this paper investigatesthe relation between near-MDS codes with some constraints and LRCs, further,proposes an algorithm to determine locality of dual of a given linearcode. Finally, based on near-MDS codes and the proposed algorithm, thoseobtained optimal LRCs are shown.