Skip to main content

Advertisement

Springer Nature Link
Log in

Construction and decoding of matrix-product codes from nested codes

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

Abstract

We consider matrix-product codes \({[C_1\cdots C_s] \cdot A}\) , where \({C_1, \ldots , C_s}\) are nested linear codes and matrix A has full rank. We compute their minimum distance and provide a decoding algorithm when A is a non-singular by columns matrix. The decoding algorithm decodes up to half of the minimum distance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Blackmore T., Norton G.H.: Matrix-product codes over \({\mathbb{F}_{q}}\) . Appl. Algebra Eng. Commun. Comput. 12(6), 477–500 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Kasami T.: A Gilbert–Varshamov bound for quasi-cyclic codes of rate 1/2. IEEE Trans. Inf. Theory 20, 679 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  3. Lally K., Fitzpatrick P.: Algebraic structure of quasicyclic codes. Discrete Appl. Math. 111(1–2), 157–175 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ling S., Solé P.: On the algebraic structure of quasi-cyclic codes I: finite fields. IEEE Trans. Inf. Theory IT-47, 2751–2759 (2001)

    Article  Google Scholar 

  5. Macwilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes, ser. North-Holland Mathematical Library, North-Holland (1977)

    Google Scholar 

  6. Martínez-Moro E.: A generalization of Niederreiter-Xing’s propagation rule and its commutativity with duality. IEEE Trans. Inf. Theory 50(4), 701–702 (2004)

    Article  Google Scholar 

  7. Niederreiter H., Xing C.: A propagation rule for linear codes. Appl. Algebra Eng. Commun. Comput. 10(6), 425–432 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Özbudak F., Stichtenoth H.: Note on Niederreiter-Xing’s propagation rule for linear codes. Appl. Algebra Eng. Commun. Comput. 13(1), 53–56 (2002)

    Article  MATH  Google Scholar 

  9. van Asch B.: Matrix-product codes over finite chain rings. Appl. Algebra Eng. Commun. Comput. 19(1), 39–49 (2008)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University College Cork, Cork, Ireland

    Fernando Hernando

  2. Department of Mathematics and Statistics, RMIT University, Melbourne, VIC, Australia

    Kristine Lally

  3. Department of Mathematics, Technical University of Denmark, Matematiktorvet, Building 303, 2800, Kgs. Lyngby, Denmark

    Diego Ruano

Authors
  1. Fernando Hernando
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Kristine Lally
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Diego Ruano
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Fernando Hernando.

Additional information

The work of F. Hernando is supported in part by the Claude Shannon Institute, Science Foundation Ireland Grant 06/MI/006 (Ireland) and by MEC MTM2007-64704 and Junta de CyL VA025A07 (Spain). The work of D. Ruano is supported in part by DTU, H.C. Oersted post doc. grant (Denmark) and by MEC MTM2007-64704 and Junta de CyL VA065A07 (Spain).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hernando, F., Lally, K. & Ruano, D. Construction and decoding of matrix-product codes from nested codes. AAECC 20, 497–507 (2009). https://doi.org/10.1007/s00200-009-0113-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00200-009-0113-5

Keywords

Mathematics Subject Classification (2000)