Skip to main content
SpringerLink
Log in

A new class of quaternary codes

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

Abstract

In this paper we introduce a new concept of modified Butson-Hadamard matrices and construct two families of quaternary codes derived from the corresponding families of modified complex matrices with entries from a finite cyclic group of order 4. These nonlinear codes have parameters lying very close to the Plotkin bound and admit very easy construction and decoding procedures.

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. Elliot, D.F. and Rao, K.R., Fast Transforms: Algorithms, Analyses, Applications, New York: Academic, 1982.

    Google Scholar 

  2. Maslen, D.K. and Rockmore, D.N., Generalized FFTs—A Survey of Some Recent Results, Groups and Computation II: Workshop on Groups and Computation, Finkelstein, L. and Kantor, W.M., Eds. Providence: AMS, 1997, pp. 183–237.

    Google Scholar 

  3. Butson, K.T., Generalized Hadamard Matrices, Proc. Amer. Math. Soc., 1962, vol. 13, pp. 894–898.

    Article  MathSciNet  Google Scholar 

  4. Baliga, A., New Self-dual Codes from Cocyclic Hadamard Matrices, J. Comb. Math. Comb. Comput., 1982, vol. 28, pp. 7–14.

    MathSciNet  Google Scholar 

  5. Baliga, A. and Horadam, K.J., Cocyclic Hadamard Matrices over ℤt × ℤ 22 , Australian J. Comb., 1995, vol. 11, pp. 123–134.

    MATH  MathSciNet  Google Scholar 

  6. Horadam, K.J. and Udaya, P., Cocyclic Hadamard Codes, IEEE Trans. Inform. Theory, 2000, vol. 46, pp. 1545–1550.

    Article  MATH  MathSciNet  Google Scholar 

  7. Pinnawala, N. and Rao, A., Cocyclic Simplex Codes of Type α over ℤ4 and ℤ2, IEEE Trans. Inform. Theory, 2004, vol. 50, no. 9, pp. 2165–2169.

    Article  MathSciNet  Google Scholar 

  8. Stepanov, S.A. and Lee, M.H., Codes from Generalized Hadamard Matrices, submitted for publication in IEEE Trans. Inform. Theory.

Download references

Author information

Authors and Affiliations

  1. Institute for Information Transmission Problems, RAS, Moscow, Russia

    S. A. Stepanov

Authors
  1. S. A. Stepanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © S.A. Stepanov, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 1, pp. 3–12.

Supported by the Institute of Information Technology Assessment (IITA), South Korea.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stepanov, S.A. A new class of quaternary codes. Probl Inf Transm 42, 1–9 (2006). https://doi.org/10.1134/S0032946006010017

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946006010017

Keywords

Search

Navigation