Skip to main content
SpringerLink
Log in

Construction of perfect q-ary codes by switchings of simple components

  • Coding Theory
  • Published:
Problems of Information Transmission Aims and scope Submit manuscript

Abstract

We suggest a construction of perfect q-ary codes by sequential switchings of special-type components (called simple components) of the Hamming code. We prove that such components are minimal. The construction yields a lower bound on the number of different q-ary codes; this is presently the best known bound. We show that this bound cannot be substantially improved using switchings of components of this type.

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. Los’, A.V., Construction of Perfect q-ary Codes by Sequential Switchings of α-Components, Probl. Peredachi Inf., 2004, vol. 40, no. 1, pp. 40–47 [Probl. Inf. Trans. (Engl. Transl.), 2004, vol. 40, no. 1, pp. 37–43].

    MathSciNet  Google Scholar 

  2. Avgustinovich, S.V. and Solov’eva, F.I., Construction of Perfect Binary Codes by Sequential Shifts of α-Components, Probl. Peredachi Inf., 1997, vol. 33, no. 3, pp. 15–21 [Probl. Inf. Trans. (Engl. Transl.), 1997, vol. 33, no. 3, pp. 202–207].

    MATH  MathSciNet  Google Scholar 

  3. Romanov, A.M., On Partitions of q-ary Hamming Codes into Disjoint Components, Diskretn. Anal. Issled. Oper., Ser. 1, 2004, vol. 11, no. 3, pp. 80–87.

    MATH  MathSciNet  Google Scholar 

  4. Los’, A.V., Construction of Perfect q-ary Codes, in Proc. 9th Int. Workshop on Algebraic and Combinatorial Coding Theory, Kranevo, Bulgaria, 2004, pp. 272–276.

  5. Phelps, K.T., Rifà, J., and Villanueva, M., Kernels of q-ary 1-Perfect Codes, in Proc. Int. Workshop on Coding and Cryptography (WCC’03), Versailles, France, 2003, pp. 375–381.

  6. Phelps, K.T. and Villanueva, M., Ranks of q-ary 1-Perfect Codes, Des. Codes Cryptogr., 2002, vol. 27, no. 1–2, pp. 139–144.

    Article  MATH  MathSciNet  Google Scholar 

  7. MacWilliams, F.J. and Sloane, N.J.A., The Theory of Error-Correcting Codes, Amsterdam: North-Holland, 1977. Translated under the title Teoriya kodov, ispravlyayushchikh oshibki, Moscow: Svyaz’, 1979.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk State University, USSR

    A. V. Los’

Authors
  1. A. V. Los’
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.V. Los’, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 1, pp. 34–42.

Supported in part by the Ministry of Education of the Russian Federation program “Development of the Scientific Potential of the Higher School,” project no. 512.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Los’, A.V. Construction of perfect q-ary codes by switchings of simple components. Probl Inf Transm 42, 30–37 (2006). https://doi.org/10.1134/S0032946006010030

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946006010030

Keywords

Search

Navigation