Skip to main content

Cyclic Additive and Quantum Stabilizer Codes

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4547))

Abstract

We develop the theory of additive cyclic codes and of cyclic quantum stabilizer codes.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ashikhmin, A., Knill, E.: Nonbinary quantum stabilizer codes. IEEE Transactions on Information Theory 47, 3065–3072 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bierbrauer, J.: The theory of cyclic codes and a generalization to additive codes. Designs, Codes and Cryptography 25, 189–206 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bierbrauer, J.: Introduction to Coding Theory, Chapman and Hall/CRC Press, Boca Raton, FL (2004)

    Google Scholar 

  4. Bierbrauer, J., Faina, G., Marcugini, S., Pambianco, F.: Additive quaternary codes of small length, Proceedings ACCT, Zvenigorod (Russia) (September 15-18, 2006)

    Google Scholar 

  5. Bierbrauer, J., Edel, Y.: Quantum twisted codes. Journal of Combinatorial Designs 8, 174–188 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Blokhuis, A., Brouwer, A.E.: Small additive quaternary codes, European Journal of Combinatorics 25, 161–167 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Transactions on Information Theory 44, 1369–1387 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Edel, Y., Bierbrauer, J.: Twisted BCH-codes. Journal of Combinatorial Designs 5, 377–389 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Edel, Y., Bierbrauer, J.: Caps of order 3q 2 in affine 4-space in characteristic 2. Finite Fields and Their Applications 10, 168–182 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Grassl, M.: Tables on http://iaks-www.ira.uka.de/home/grassl/

  11. Rains, E.M.: Nonbinary quantum codes. IEEE Transactions on Information Theory 45, 1827–1832 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Schoof, R., van der Vlugt, M.: Hecke operators and the weight distribution of certain codes. Journal of Combinatorial Theory A 57, 163–186 (1991)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Claude Carlet Berk Sunar

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bierbrauer, J. (2007). Cyclic Additive and Quantum Stabilizer Codes. In: Carlet, C., Sunar, B. (eds) Arithmetic of Finite Fields. WAIFI 2007. Lecture Notes in Computer Science, vol 4547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73074-3_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73074-3_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73073-6

  • Online ISBN: 978-3-540-73074-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics