Bounds on Fractional Repetition Codes using Hypergraphs

In the Distributed Storage Systems (DSSs), encoded fraction of information is stored in the distributed fashion on different chunk servers. Recently a new paradigm of Fractional Repetition (FR) codes have been introduced, in which, encoded data information is stored on distributed servers, where encoding is done using a Maximum Distance Separable (MDS) code and a repetition code. In this work, we have shown that an FR code is equivalent to a hypergraph. Using the correspondence, the properties and the bounds of a hypergraph are directly mapped to the associated FR code. Some of the bounds are not satisfied by any FR codes in the literature with equality. In general, the necessary and sufficient conditions for the existence of an FR code is obtained by using the correspondence. It is also shown that any FR code associated with a linear hypergraph is universally good.