Skip to main content
SpringerLink
Log in

Inductive Constructions of Perfect Ternary Constant-Weight Codes with Distance 3

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

Abstract

We propose inductive constructions of perfect (n,3;n – 1)3 codes (ternary constant-weight codes of length n and weight n – 1 with distance 3), which are modifications of constructions of perfect binary codes. The construction yields at least \(2^{2^{n/2 - 2} }\) different perfect (n,3;n – 1)3 codes. To perfect (n,3;n – 1)3 codes, perfect matchings in a binary hypercube without close (at distance 1 or 2 from each other) parallel edges are equivalent.

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. Svanström, M., Ternary Codes with Weight Constraints, Dissertation no. 572, Linköping: Linköping Univ., 1999.

    Google Scholar 

  2. Svanström, M., A Class of Perfect Ternary Constant-Weight Codes, Designs, Codes and Cryptography, 1999, vol. 18,nos. 1–3, pp. 223-230.

    Google Scholar 

  3. van Lint, J. and Tolhuizen, L., On Perfect Ternary Constant-Weight Codes, Designs, Codes and Cryptography, 1999, vol. 18,nos. 1–3, pp. 231-234.

    Google Scholar 

  4. Krotov, D.S., Combining Construction of Perfect Binary Codes and of Perfect Ternary Constant-Weight Codes, in Proc. 7th Int. Workshop on Algebr. Combin. Coding Theory, Bansko, Bulgaria, 2000, pp. 193-198.

  5. Krotov, D.S., Combining Construction of Perfect Binary Codes, Probl. Peredachi Inf., 2000, vol. 36,no. 4, pp. 74-79 [Probl. Inf. Trans. (Engl. Transl.), 2000, vol. 36, no. 4, pp. 349–353].

    Google Scholar 

  6. 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.

    Google Scholar 

  7. Hamburger, P., Pippert, R.E., and Weakley, W.D., On a Leverage Problem in the Hypercube, Networks, 1992, vol. 22, pp. 435-439.

    Google Scholar 

  8. Mollard, M., A Generalized Parity Function and Its Use in the Construction of Perfect Codes, SIAM J. Algebr. Discrete Methods, 1986, vol. 7,no. 1, pp. 113-115.

    Google Scholar 

  9. Phelps, K.T., A General Product Construction for Error Correcting Codes, SIAM J. Algebr. Discrete Methods, 1984, vol. 5,no. 2, pp. 224-228.

    Google Scholar 

  10. Lobstein, A.C. and Zinoviev, V.A., On New Perfect Binary Nonlinear Codes, Appl. Algebra Eng. Commun. Comput., 1997, vol. 8, pp. 415-420.

    Google Scholar 

  11. Zinoviev, V.A. and Lobstein, A.C., Constructions of Perfect Binary Nonlinear Codes, in Proc. 6th Int. Workshop on Algebr. Combin. Coding Theory, Pskov, Russia, 1998, pp. 249-254.

  12. Zinoviev, V.A., On Generalized Concatenated Codes, Colloquia Mathematica Societatis János Bolyai, 1995, vol. 16, pp. 587-592.

    Google Scholar 

  13. Vasil'ev, Yu.L., On Nongroup Closely Packed Codes, Probl. Kibern., 1962, vol. 8, pp. 337-339.

    Google Scholar 

Download references

Authors
  1. D. S. Krotov
    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

Krotov, D.S. Inductive Constructions of Perfect Ternary Constant-Weight Codes with Distance 3. Problems of Information Transmission 37, 1–9 (2001). https://doi.org/10.1023/A:1010424208992

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010424208992

Keywords

Search

Navigation