Skip to main content

Advertisement

Log in

Bounds and constructions of asymmetric or unidirectional error-correcting codes

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Binary block codes for correctingt symmetric, asymmetric and unidirectional errors are calledt-SyEC codes,t-AsEC codes andt-UEC codes respectively. Two tables with bounds on the cardinality of binary block codes for correcting asymmetric and unidirectional errors respectively are presented. They include many improvements over the existing literature. The lower bounds follow from explicit constructions, while the upper bounds are obtained by applying combinatorial arguments to the weight structure of such codes.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Bose, B., Rao, T. R. N.: Theory of unidirectional error correcting/detecting codes. IEEE Trans. Comput.31, 521–530 (1982)

    Google Scholar 

  2. Brouwer, A. E., Shearer, J. B., Sloane, N. J. A., Smith, W. D.: A new table of constant weight codes. IEEE Trans. Inform. Theory IT-36, 1334–1380 (1990)

    Google Scholar 

  3. Brouwer, A. E.: Private communication

  4. Bussemaker, F. C., Mathon, R. A., Seidel, J. J.: Tables of two-graphs. T.H.-Report 79-WSK-05, Eindhoven University of Technology, October 1979

  5. Delsarte, P., Piret, P.: Bounds and constructions for binary asymmetric error-correcting codes, IEEE Trans. Inf. TheoryIT-27, 125–128 (1981); correction, vol. 36(4), p. 954, (1990)

    Google Scholar 

  6. Etzion, T.: New lower bounds for asymmetric and unidirectional codes, IEEE Trans. Infor. TheoryIT-37, 1696–1704 (1991)

    Google Scholar 

  7. Fang, G., van Tilborg, H. C. A.: Uniqueness of 1-AsEc codes for length ≦ 8. Preprint

  8. Fang, G., van Tilborg, H. C. A.: New tables of AsEC and UEC codes. EUT Report 91-WSK-02, Eindhoven University of Technology, The Netherlands 1991

    Google Scholar 

  9. Hall, Jr., M.: Combinatorial Theory. New York: John Wiley 1986

    Google Scholar 

  10. Honkala, I. S.: Some lower bounds for constant weight codes. Discrete Appl. Math.18, 95–98 (1987)

    Google Scholar 

  11. Kim, W. H., Freiman, C. V.: Single error-correcting codes for asymmetric binary channels, IRE Trans. Inform. TheoryIT-5, 62–66 (1959)

    Google Scholar 

  12. Kløve, T.: Error correcting codes for the asymmetric channel. Rep. 18-09-07-81, Department of Mathematics, University of Bergen, Norway, July 1981

    Google Scholar 

  13. —: Upper bounds on codes correcting asymmetric errors. IEEE Trans. Inform. Theory IT-27(1), 128–131 (1981)

    Google Scholar 

  14. MacWilliams, F. J., Sloane, N. J. A.: The Theory of Error-Correcting Codes. Amsterdam: North-Holland 1979

    Google Scholar 

  15. Rao, T. R. N. Fujiwara, E.: Error-Control coding for Computer Systems. Prentice-Hall, Englewood Cliffs, New Jersey 1989

    Google Scholar 

  16. Saitoh, Y., Yamaguchi, K., Imai, H.: Some new binary codes correcting asymmetric/unidirectional errors. IEEE Trans. Inform. Theory IT-36, 645–647 (1990)

    Google Scholar 

  17. Sloane, N. J. A., Seidel, J. J.: A new family of nonlinear codes obtained from conference matrices. Ann. NY Acad. Sci.175, 363–365 (1970)

    Google Scholar 

  18. Van Lint, J. H., Weber, J. H.: Some combinatorial codes for the binary asymmetric channel, Preprint

  19. Weber, J. H.: Bounds and constructions for binary block codes correcting asymmetric or unidirectional errrors. The Ph.D. dissertation, Department of Electrical Engineering of Delft University of Technology, The Netherlands 1989

    Google Scholar 

  20. Weber, J. H., de Vroedt, C., Boekee, D. E.: New upper bounds on the size of codes correcting asymmetric errors. IEEE Trans. Inform. Theory IT-33, 434–437 (1987)

    Google Scholar 

  21. —: Bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6. IEEE Trans. Inform. Theory IT-34, 1321–1331 (1988)

    Google Scholar 

  22. —: Bounds and constructions for codes correcting unidirectional errors, IEEE Trans. Inform. TheoryIT-35, 797–810 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fang, G., van Tilborg, H.C.A. Bounds and constructions of asymmetric or unidirectional error-correcting codes. AAECC 3, 269–300 (1992). https://doi.org/10.1007/BF01294837

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01294837

Keywords