Skip to main content

A Short Introduction to Cyclic Convolutional Codes

  • Chapter
  • First Online:
Gröbner Bases, Coding, and Cryptography

Abstract

We introduce the notion of cyclic convolutional codes and briefly survey some recent results that were derived with the aid of Gröbner-type theory.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • H. Gluesing-Luerssen and B. Langfeld, A class of one-dimensional MDS convolutional codes, J. Algebra Appl. 5 (2006a), no. 4, 505–520.

    Article  MathSciNet  MATH  Google Scholar 

  • H. Gluesing-Luerssen and B. Langfeld, On the algebraic parameters of convolutional codes with cyclic structure, J. Algebra Appl. 5 (2006b), no. 1, 53–76.

    Article  MathSciNet  MATH  Google Scholar 

  • H. Gluesing-Luerssen and W. Schmale, On cyclic convolutional codes, Acta Appl. Math. 82 (2004), no. 2, 183–237.

    Article  MathSciNet  MATH  Google Scholar 

  • H. Gluesing-Luerssen and W. Schmale, On doubly-cyclic convolutional codes, AAECC 17 (2006), no. 2, 151–170.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Giorgetti, M. Rossi, and M. Sala, On the Gröbner basis of a family of quasi-cyclic LDPC codes, Bull. Iran. Math. Soc. 31 (2005), no. 2, 13–32.

    MathSciNet  MATH  Google Scholar 

  • W. C. Huffman and V. Pless, Fundamentals of error-correcting codes, Cambridge University Press, Cambridge, 2003.

    MATH  Google Scholar 

  • K. Lally, Canonical representation of quasicyclic codes using Gröbner basis theory, this volume, 2009, pp. 351–355.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • R. J. McEliece, The algebraic theory of convolutional codes, Handbook of Coding Theory, vol. 1, Elsevier, Amsterdam, 1998, pp. 1065–1138.

    Google Scholar 

  • P. Piret, Structure and constructions of cyclic convolutional codes, IEEE Trans. on Inf. Th. 22 (1976), no. 2, 147–155.

    Article  MathSciNet  MATH  Google Scholar 

  • C. Roos, On the structure of convolutional and cyclic convolutional codes, IEEE Trans. on Inf. Th. 25 (1979), no. 6, 676–683.

    Article  MathSciNet  MATH  Google Scholar 

  • J. Rosenthal and R. Smarandache, Maximum distance separable convolutional codes, AAECC 10 (1999), no. 1, 15–32.

    Article  MathSciNet  MATH  Google Scholar 

  • G. Solomon and H. C. A. van Tilborg, A connection between block and convolutional codes, SIAM J. Appl. Math. 37 (1979), no. 2, 358–369.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Heide Gluesing-Luerssen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gluesing-Luerssen, H., Langfeld, B., Schmale, W. (2009). A Short Introduction to Cyclic Convolutional Codes. In: Sala, M., Sakata, S., Mora, T., Traverso, C., Perret, L. (eds) Gröbner Bases, Coding, and Cryptography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93806-4_29

Download citation

Publish with us

Policies and ethics