Skip to main content
SpringerLink
Log in

Symmetric Block Designs and Optimal Equidistant Codes

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

Abstract

We prove that any symmetric block design (v, k, λ) generates optimal ternary and quaternary constant-weight equidistant codes, whose parameters n, N, w, d, q are uniquely determined by the parameters of the block design. For one rather special case, we construct symbolwise uniform equidistant codes of the minimum length.

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. Bassalygo, L.A., New Upper Bounds for Error Correcting Codes, Probl. Peredachi Inf., 1965, vol. 1, no. 4, pp. 41–44 [Probl. Inf. Transm. (Engl. Transl.), 1965, vol. 1, no. 4, pp. 32–35].

    MathSciNet  MATH  Google Scholar 

  2. Semakov, N.V. and Zinoviev, V.A., Equidistant q-ary Codes with Maximal Distance and Resolvable Balanced Incomplete Block Designs, Probl. Peredachi Inf., 1968, vol. 4, no. 2, pp. 3–10 [Probl. Inf. Transm. (Engl. Transl.), 1968, vol. 4, no. 2, pp. 1–7].

    MathSciNet  MATH  Google Scholar 

  3. Beth, T., Jungnickel, D., and Lenz, H., Design Theory, 2 vols., Cambridge: Cambridge Univ. Press, 1999, 2nd ed.

    Book  Google Scholar 

  4. Sinha, K. and Sinha, N., A Class of Optimal Quaternary Codes, Ars Combin., 2010, vol. 94, pp. 61–64.

    MathSciNet  MATH  Google Scholar 

  5. Bassalygo, L.A. and Zinoviev, V.A., Remark on Balanced Incomplete Block Designs, Near-Resolvable Block Designs, and q-ary Constant-Weight Codes, Probl. Peredachi Inf., 2017, vol. 53, no. 1, pp. 55–58 [Probl. Inf. Transm. (Engl. Transl.), 2017, vol. 53, no. 1, pp. 51–54].

    MathSciNet  Google Scholar 

  6. Bassalygo, L.A., Zinoviev, V.A., and Lebedev, V.S., On m-Near-Resolvable Block Designs and q-ary Constant-Weight Codes, Probl. Peredachi Inf., 2018, vol. 54, no. 3, pp. 54–61 [Probl. Inf. Transm. (Engl. Transl.), 2018, vol. 54, no. 3, pp. 245–252].

    MathSciNet  Google Scholar 

  7. Semakov, N.V., Zinoviev, V.A., and Zaitsev, G.V., A Class of Maximum Equidistant Codes, Probl. Peredachi Inf., 1969, vol. 5, no. 2, pp. 84–87 [Probl. Inf. Transm. (Engl. Transl.), 1969, vol. 5, no. 2, pp. 65–68].

    MathSciNet  MATH  Google Scholar 

Download references

Funding

Supported in part by the Russian Foundation for Basic Research, project no. 19-01-00364.

Author information

Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    L. A. Bassalygo, V. A. Zinoviev & V. S. Lebedev

Authors
  1. L. A. Bassalygo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Zinoviev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. S. Lebedev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bassalygo, L., Zinoviev, V. & Lebedev, V. Symmetric Block Designs and Optimal Equidistant Codes. Probl Inf Transm 56, 245–252 (2020). https://doi.org/10.1134/S0032946020030023

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946020030023

Keywords

Search

Navigation