Constructions of Binary Codes Based on Bipartite Graphs

Abstract

In this paper, we construct some families of binary linear and nonlinear codes by using various bipartite graphs. Furthermore, we also determine some conditions for the constructed binary linear code to be a maximum distance separable code.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Asratian, A.S., Denley, M.J.T., Hggkvist, R.: Bipartite graphs and their applications. In: Cambridge Tracts in Mathematics, vol. 131. Cambridge University Press, Cambridge (1998)

  2. 2.

    Gross, J.L., Yellen, J.: Graph theory and its applications. In: Discrete Mathematics and its Applications, 2nd edn. CRC Press, Boca Raton (2005)

  3. 3.

    Moon, K.T.: Error Correction Coding: Mathematical Methods and Algorithms. Wiley, New York (2005)

    Google Scholar 

  4. 4.

    Sloane, N.J.A., Macwilliam, F.J.: The Theory of Error Correcting Codes. North-Holland, Amsterdam (1978)

    Google Scholar 

  5. 5.

    Wilson, R.J.: Introduction to Graph Theory. Longman, Hong Kong (1972)

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Denis C. K. Wong.

Additional information

This work was completed with the support of UTAR funding.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wong, D.C.K. Constructions of Binary Codes Based on Bipartite Graphs . Math.Comput.Sci. 10, 223–227 (2016). https://doi.org/10.1007/s11786-016-0258-0

Download citation

Keywords

  • Linear codes
  • Bipartite graphs
  • Minimum distance

Mathematics Subject Classification

  • Primary 14G50
  • Secondary 57M15