On the Optimal Minimum Distance of Fractional Repetition Codes

Abstract: Fractional repetition (FR) codes are a class of repair efficient erasure codes that can recover a failed storage node with both optimal repair bandwidth and complexity. In this paper, we study the minimum distance of FR codes, which is the smallest number of nodes whose failure leads to the unrecoverable loss of the stored file. We consider upper bounds on the minimum distance and present several families of explicit FR codes attaining these bounds. The optimal constructions are derived from regular graphs and combinatorial designs, respectively.