In the Distributed Storage Systems (DSSs), the encoded fraction of information is stored in a distributed fashion on different chunk servers. Recently a new paradigm of Fractional Repetition (FR) codes has been introduced, in which, encoded data information is stored on distributed servers using an encoding involving a Maximum Distance Separable (MDS) code and a Repetition code. In this work, we have considered FR codes with asymmetric parameters known as Generalized Fractional Repetition (GFR) codes. We have shown that any GFR code is equivalent to a hypergraph. Using the correspondence, the properties and the bounds of a hypergraph are directly mapped to the associated GFR code. In general, using the correspondence, the necessary and sufficient conditions for the existence of a GFR code is obtained. It is also shown that any GFR code associated with a linear hypergraph is universally good, and any locally repairable GFR code is associated with a class of non-linear hypergraph.

在分布式存储系统（DSS）中，信息的编码部分以分布式方式存储在不同的块服务器上。最近，引入了新的分数重复（FR）码范例，其中，编码数据信息使用涉及最大距离可分离（MDS）码和重复码的编码存储在分布式服务器上。在这项工作中，我们考虑了具有非对称参数的FR码，称为广义分数重复（GFR）代码。我们已经表明，任何GFR代码都等效于一个超图。使用对应关系，超图的属性和边界直接映射到关联的GFR代码。通常，使用该对应关系，获得存在GFR码的必要和充分条件。还显示出，与线性超图相关联的任何GFR代码普遍良好，并且任何可局部修复的GFR代码与一类非线性超图相关联。