  Fractional repetition (FR) codes is a family of codes for distributed storage
systems (DSS) that allow uncoded exact repairs with 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, such as Tur\'an graphs and graphs with large girth; and on
combinatorial designs, such as transversal designs and generalized polygons. In
addition, based on a connection between FR codes and batch codes, we propose a
new family of codes for DSS, called fractional repetition batch codes, which
allow uncoded efficient exact repairs and load balancing which can be performed
by several users in parallel.
