Subspace Codes | SpringerLink
Skip to main content

Subspace Codes

  • Conference paper
Cryptography and Coding (IMACC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5921))

Included in the following conference series:

Abstract

This paper is a survey of bounds and constructions for subspace codes designed for the injection metric, a distance measure that arises in the context of correcting adversarial packet insertions in linear network coding. The construction of lifted rank-metric codes is reviewed, along with improved constructions leading to codes with strictly more codewords. Algorithms for encoding and decoding are also briefly described.

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

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 11439
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 14299
Price includes VAT (Japan)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Kötter, R., Kschischang, F.R.: Coding for errors and erasures in random network coding. IEEE Trans. Inf. Theory 54(8), 3579–3591 (2008)

    Article  Google Scholar 

  2. Silva, D., Kschischang, F.R.: On metrics for error correction in network coding. IEEE Trans. Inf. Theory (to appear 2009)

    Google Scholar 

  3. Silva, D., Kschischang, F.R., Kötter, R.: A rank-metric approach to error control in random network coding. IEEE Trans. Inf. Theory 54(9), 3951–3967 (2008)

    Article  Google Scholar 

  4. Silva, D., Kschischang, F.R.: Universal secure network coding via rank-metric codes. IEEE Trans. Inf. Theory (2008) (submitted for publication)

    Google Scholar 

  5. Katti, S., Katabi, D., Balakrishnan, H., Médard, M.: Symbol-level network coding for wireless mesh networks. In: ACM SIGCOMM, Seattle, WA (August 2008)

    Google Scholar 

  6. Wang, H., Xing, C., Safavi-Naini, R.: Linear authentication codes: bounds and constructions. IEEE Trans. Inf. Theory 49(4), 866–872 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Xia, S.T., Fu, F.W.: Johnson type bounds on constant dimension codes. Designs, Codes and Cryptography 50(2), 163–172 (2009)

    Article  MathSciNet  Google Scholar 

  8. Borel, A.: Linear Algebraic Groups. In: Grad. Texts Math., 2nd edn., vol. 126. Springer, Heidelberg (1991)

    Google Scholar 

  9. Brouwer, A.E., Cohen, A.M., Neumaier, A.: Distance-Regular Graphs. Springer, New York (1989)

    MATH  Google Scholar 

  10. van Lint, J.H., Wilson, R.M.: A Course in Combinatorics, 2nd edn. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  11. Gabidulin, E.M.: Theory of codes with maximum rank distance. Probl. Inform. Transm. 21(1), 1–12 (1985)

    MATH  Google Scholar 

  12. Delsarte, P.: Bilinear forms over a finite field, with applications to coding theory. J. of Comb. Theory. Series A 25, 226–241 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  13. Loidreau, P.: Étude et optimisation de cryptosystèmes à clé publique fondés sur la théorie des codes correcteurs. Ph.d. dissertation, École Polytechnique, Paris, France (May 2001)

    Google Scholar 

  14. Gadouleau, M., Yan, Z.: Packing and covering properties of cdcs and subspace codes. IEEE Trans. on Inform. Theory (2008) (Submitted)

    Google Scholar 

  15. Delsarte, P.: An algebraic approach to association schemes of coding theory. Philips J. Res., 1–97 (1973)

    Google Scholar 

  16. Frankl, P., Wilson, R.: The Erdös-Ko-Rado Theorem for Vector Spaces. Journal of Combinatorial Theory 43, 228–236 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  17. Etzion, T., Vardy, A.: Error-correcting codes in projective space. In: Proc. IEEE Int. Symp. Information Theory, Toronto, Canada, July 6-11, pp. 871–875 (2008)

    Google Scholar 

  18. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)

    MATH  Google Scholar 

  19. Ahlswede, R., Aydinian, H.: On error control for random network coding. In: IEEE Workshop on Network Coding, Theory and Applications (2009)

    Google Scholar 

  20. Khaleghi, A., Kschischang, F.R.: Projective space codes for the injection metric. In: Proc. 11th Canadian Workshop Inform. Theory, Ottawa, May 13-15, pp. 9–12 (2009)

    Google Scholar 

  21. Tolhuizen, L.M.G.M.: The generalized Gilbert-Varshamov bound is implied by Túran’s theorem. IEEE Trans. Inf. Theory 43(5), 1605–1606 (1997)

    Article  MathSciNet  Google Scholar 

  22. Silva, D.: Error Control for Network Coding. PhD thesis, University of Toronto, Toronto, Canada (2009)

    Google Scholar 

  23. Skachek, V.: Recursive code construction for random networks. Submitted for Publication (2008)

    Google Scholar 

  24. Manganiello, F., Gorla, E., Rosenthal, J.: Spread codes and spread decoding in network coding. In: Proc. IEEE Int. Symp. Information Theory, Toronto, Canada, July 6-11, pp. 881–885 (2008)

    Google Scholar 

  25. Gabidulin, E., Bossert, M.: Codes for network coding. In: Proc. IEEE Int. Symp. Information Theory, Toronto, Canada, July 6-11, pp. 867–870 (2008)

    Google Scholar 

  26. Etzion, T., Silberstein, N.: Error-correcting codes in projective spaces via rank-metric codes and Ferrers diagrams. IEEE Trans. Inf. Theory 55(7), 2909–2919 (2009)

    Article  Google Scholar 

  27. Khaleghi, A.: Projective space codes for the injection metric. Master’s thesis, University of Toronto, Toronto, Canada (2009)

    Google Scholar 

  28. Kohnert, A., Kurz, S.: Construction of large constant dimension codes with a prescribed minimum distance. Mathematical Methods in Computer Science: Essays in Memory of Thomas Beth, 31–42 (2008)

    Google Scholar 

  29. Silva, D., Kschischang, F.R.: Fast encoding and decoding of Gabidulin codes. In: Proc. IEEE Int. Symp. Information Theory, Seoul, Korea, June 28-July 3, pp. 2858–2862 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Khaleghi, A., Silva, D., Kschischang, F.R. (2009). Subspace Codes. In: Parker, M.G. (eds) Cryptography and Coding. IMACC 2009. Lecture Notes in Computer Science, vol 5921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10868-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-10868-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10867-9

  • Online ISBN: 978-3-642-10868-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics