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

Document Type : Original Article

Authors

1 Payame Noor University

2 Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman

3 Faculty of Mathematics, Payme Noor University

4 Department of Mathematics, Faculty of Basic Sciences, Payame Noor University, Tehran, Iran

Abstract

In this paper, we call a hypergraph constructed by (non) binary linear\nonlinear 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 linear\nonlinear 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. 

Keywords

References

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History

  • Receive Date: 30 April 2019
  • Revise Date: 04 July 2019
  • Accept Date: 02 October 2019
  • Publish Date: 02 March 2020

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