Skip to main content
SpringerLink
Log in

On the Minimum Distances of Non-Binary Cyclic Codes

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

We deal with the minimum distances of q-ary cyclic codes of length q m - 1 generated by products of two distinct minimal polynomials, give a necessary and sufficient condition for the case that the minimum distance is two, show that the minimum distance is at most three if q > 3, and consider also the case q = 3.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Charpin, A. Tietäväinen and V. Zinoviev, On binary cyclic codes with minimum distance three, Problems of Information Transmission, Vol. 33 (1997) pp. 3-14.

    Google Scholar 

  2. H. Janwa, G. McGuire and R.M. Wilson, Double-error-correcting cyclic codes and absolutely irreducible polynomials over GF(2), Journal of Algebra, Vol. 178 (1995) pp. 665-676.

    Google Scholar 

  3. J. H. van Lint and R. M. Wilson, On the minimum distance of cyclic codes, IEEE Transactions on Information Theory, Vol. 32 (1986) pp. 23-40.

    Google Scholar 

  4. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, New York (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INRIA, Codes Domaine de Voluceau-Rocquencourt, BP 105 - 78153, Le Chesnay, France

    Pascale Charpin

  2. Department of Mathematics and, TUCS University of Turku, FIN-20014, Turku, Finland

    Aimo Tietäväinen

  3. Institute for Problems of Information Transmission of the, Russian Academy of Sciences, Bol'shoi Karetnyi 19 GSP-4, Moscow, 101447, Russia

    Victor Zinoviev

Authors
  1. Pascale Charpin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aimo Tietäväinen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Victor Zinoviev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Charpin, P., Tietäväinen, A. & Zinoviev, V. On the Minimum Distances of Non-Binary Cyclic Codes. Designs, Codes and Cryptography 17, 81–85 (1999). https://doi.org/10.1023/A:1008354504832

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008354504832

Search

Navigation