Optimal fractional repetition codes for distributed storage systems

Fractional repetition (FR) codes is a family of codes for distributed storage systems that allow for uncoded exact repairs having the minimum repair bandwidth. In this work, we consider a bound on the maximum amount of data that can be stored using an FR code. Optimal FR codes which attain this bound are presented. The constructions of these FR codes are based on families of regular graphs, namely, Turán graphs and graphs with large girth and on combinatorial designs, namely transversal designs and generalized polygons.