Graph Based Approach for Error-Detecting and Correcting Codes

Authors

R. El-Shanawany, Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, EgyptFollow
S. A. El-Sheikh, Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, EgyptFollow
S. A. El-Sheikh, Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, EgyptFollow
S. R. Halawa, Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, EgyptFollow
H. Shabana, Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

Combinatorial designs have properties that make them a significant tool for constructing good error detecting or correcting codes. In this paper, we use the fundamental properties of the incidence matrix of the graph designs (H , G, l ) to construct some efficient error detecting and correcting codes. In this manner, we consider H a regular graph, G a subgraph of H and l ≥ 2 to be an integer number. A (H,G,l) design is a collection of subgraphs G1,G2,··· ,Gb of H with each Gi ≃ G;i ∈ {1,2,···b}, every edge from H appears exactly l times in that design and any two subgraphs Gi,Gj are orthogonal (have at most on edge common). We propose an approach that can generate an (H,G,l) design for some G and different H. Whenever building such a design, block graph binary codes are generated from the incidence matrix of such design. The resulting codes can be shown to be hamming codes with weights divisible by the cardinality of the edge set of G and the inner product of any two codewords ≤ 1. Using the minimum hamming distance of the constructed codes, one can efficiently detect and correct errors.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/160616

Recommended Citation

El-Shanawany, R.; A. El-Sheikh, S.; A. El-Sheikh, S.; R. Halawa, S.; and Shabana, H. (2022) "Graph Based Approach for Error-Detecting and Correcting Codes," Applied Mathematics & Information Sciences: Vol. 16: Iss. 5, Article 16.
DOI: http://dx.doi.org/10.18576/amis/160616
Available at: https://digitalcommons.aaru.edu.jo/amis/vol16/iss5/16