On the Kronecker Product Construction of Completely Transitive q-Ary Codes | SpringerLink
Skip to main content
Springer Nature Link
Log in

On the Kronecker Product Construction of Completely Transitive q-Ary Codes

  • Conference paper
Coding Theory and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5228))

  • 760 Accesses

Abstract

For any integer ρ ≥ 1 and for any prime power q, the explicit construction of an infinite family of completely transitive (and completely regular) q-ary codes with minimum distance d = 3 and with covering radius ρ is given.

This work has been partially supported by the Spanish MEC and the European FEDER Grants MTM2006-03250 and TSI2006-14005-C02-01 and also by the Russian fund of fundamental researches (the number of project 06 - 01 - 00226).

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Borges, J., Rifa, J., Zinoviev, V.A.: On non-antipodal binary completely regular codes. Discrete Mathematics 308(16), 3508–3525 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Brouwer, A.E., Cohen, A.M., Neumaier, A.: Distance-Regular Graphs. Springer, Berlin (1989)

    MATH  Google Scholar 

  3. Cohen, G., Honkala, I., Litsyn, S., Lobstein, A.: Covering Codes. Elsevier, Amsterdam (1997)

    MATH  Google Scholar 

  4. Delsarte, P.: An algebraic approach to the association schemes of coding theory. Philips Research Reports Supplements 10 (1973)

    Google Scholar 

  5. Giudici, M., Praeger, C.E.: Completely Transitive Codes in Hamming Graphs. Europ. J. Combinatorics 20, 647–662 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error Correcting Codes. North-Holland, New York (1977)

    MATH  Google Scholar 

  7. Neumaier, A.: Completely regular codes. Discrete Maths. 106/107, 335–360 (1992)

    MathSciNet  Google Scholar 

  8. Rifa, J., Zinoviev, V.A.: On new completely regular q-ary codes. Problems of Information Transmission 43(2) (2007)

    Google Scholar 

  9. Rifa, J., Zinoviev, V.A.: On new completely regular codes from perfect codes. In: Proceedings of the Tenth Intern. Workshop on Algebraic and Combinatorial Coding Theory (ACCT-X), Zvenigorod, Russia, September 03-09 (2006)

    Google Scholar 

  10. Solé, P.: Completely Regular Codes and Completely Transitive Codes. Discrete Maths. 81, 193–201 (1990)

    Article  MATH  Google Scholar 

  11. Semakov, N.V., Zinoviev, V.A., Zaitsev, G.V.: Class of maximal equidistant codes. Problems of Information Transmission 5(2), 84–87 (1969)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Information and Communications Engineering, Universitat Autònoma de Barcelona, Spain

    Josep Rifà

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

    Victor Zinoviev

Authors
  1. Josep Rifà
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Victor Zinoviev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ángela Barbero

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rifà, J., Zinoviev, V. (2008). On the Kronecker Product Construction of Completely Transitive q-Ary Codes. In: Barbero, Á. (eds) Coding Theory and Applications. Lecture Notes in Computer Science, vol 5228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87448-5_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-87448-5_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87447-8

  • Online ISBN: 978-3-540-87448-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics