1Explicit MBR All-Symbol Locality Codes

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously. I. BACKGROUND A. Vector Codes An [n,K, dmin, α] vector code over a field Fq is a code C of block length n, having a symbol alphabet Fαq for some α> 1, satisfying the additional property that given c, c ′ ∈ C and a, b ∈ Fq, ac+ bc ′ also belongs to C. As a vector space over Fq, C has dimension K, termed the scalar dimension (equivalently, the file size) of the code and as a code over the alphabet Fαq, the code has minimum distance dmin