Some Constructions of Optimal Locally Repairable Codes
Wentu Song, Kui Cai · 2018
Codes with locality, also known as locally repairable codes (LRC), are designed for distributed storage systems (DSS) to reduce the disk I/O complexity for node repair. A linear code is said to have (r, δ)-locality if each code symbol is contained in a local code of length ≤ r + δ - 1 and minimum distance ≥ δ. For such codes, a generalized Singleton bound of the minimum distance was proven by Prakash et al (ISIT'12).In this paper, we consider the problem of constructing optimal codes with (r, δ)-locality. Specifically, we present three classes of linear codes that have (r, δ)-locality and whose minimum distance achieves the generalized Singleton bound. For δ = 2, we provide a combinatorial description of the largest possible d such that there exists a linear code with (r, δ)-locality and minimum distance d.