Structure of code-based hypergraphs and their application in wireless sensor networks

In this paper, we call a hypergraph constructed by (non) binary linearnonlinear codes a code-based hypergraph and study its properties. A transitive equivalence relation on any arbitrary code (as vertices) and its equivalence classes is defined as hyperedges of a hypergraph. This transitive relation, transfers the original information considered as a special code from the source in a form of subsets of special codes to hyper edges and therefore as a result, it puts each hyper edge in a one to one correspondence with a subset of special code. This research, shows that any transitive equivalence relation on codes provides a code-based hypergraph structure, and the significance of this topic is that the information in the form of linearnonlinear codes can be transferred in different ways. Finally, this study relates code-based hypergraphs to code-based graphs via a binary relation, so that one could study and use its importance and application in different networks. In addition, one example of its application is introduced and described in wireless sensor networks.