Skip to main content
SpringerLink
Log in

Construction of binary minimal product parity-check matrices

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

A parity-check matrix H of a given code \({\mathcal{C}}\) is called minimal if it has minimum number of nonzero entries among all parity-check matrices representing \({\mathcal{C}}\) . Let \({\mathcal{C}_1}\) and \({\mathcal{C}_2}\) be two binary linear block codes with minimal parity-check matrices H 1 and H 2, respectively. It is shown that, using H 1 and H 2, one can efficiently generate a minimal parity-check matrix for the product code \({\mathcal{C}_1\otimes\mathcal{C}_2}\) .

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. Berlekamp, E.R.: Algebraic Coding Theory. McGraw-Hill, (1968)

    MATH  Google Scholar 

  2. Elias, P.: Error-free coding. IRE Trans. Inf. Theory. 29-37 (1954)

  3. Hagenauer, J., Offer, E., Papke, L.: Iterative decoding of binary block and convolutional codes. IEEE Trans. Inform. Theory 42, 429– (1996)

    Article  MATH  Google Scholar 

  4. Lodge, J., Young, R., Hoeher, P., Hagenauer, J.: Separable MAP filters for the decoding of product and concatenated codes. In: Proc. IEEE ICC, Geneva, Switzerland, pp. 1740–1745 (1993)

  5. McEliece, R.J., MacKay, D.J.C, Cheng, J.-F.: Turbo decoding as an instance of Pearl’s belief propagation algorithm. IEEE J. Select. Areas Commun. 16, 140– (1998)

    Article  Google Scholar 

  6. Roth, R.M.: Introduction to Coding Theory. Cambridge University Press, (2006)

    MATH  Google Scholar 

  7. Tanner, R.M.: A recursive approach to low complexity codes. IEEE Trans. Inform. Theory 27, 533– (1981)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    Morteza Esmaeili

  2. Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran

    Morteza Esmaeili

Authors
  1. Morteza Esmaeili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Morteza Esmaeili.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Esmaeili, M. Construction of binary minimal product parity-check matrices. AAECC 19, 339–348 (2008). https://doi.org/10.1007/s00200-008-0069-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00200-008-0069-x

Keywords

Search

Navigation