Locally Repairable Regenerating Code Constructions

In this work, we give locally repairable regenerating code (LRRC) [1]–[4] constructions that can protect the file size promised by the graph analysis of the modified family helper selection (MFHS) scheme [1] at the minimum-bandwidthregenerating (MBR) point. I. RANDOM LINEAR CODE CONSTRUCTION FOR A CLASS OF (n, k, d, r) PARAMETERS In this section, we prove the existence and construction of linear locally repairable regenerating codes (LRRCs) that achieve the MBR point of the MFHS scheme for (n, k, d, r) values that satisfy that n−d−r = 2 and n mod (n−d−r) = 0, i.e., the family size in the MFHS scheme is 2 and there are no incomplete families. The code existence proof idea and construction are inspired by the work in [7]. The goal of this section is to prove the existence and construction of linear codes that can protect a file of size