Skip to main content
Log in

On covering sets for limited-magnitude errors

  • Published:
Cryptography and Communications Aims and scope Submit manuscript

Abstract

The concepts of a linear covering code and a covering set for the limited-magnitude-error channel were introduced in Kløve and Schwartz (2013). Here, a number of new covering set constructions are given, in particular for sets of r-tuples of large r. The main emphasis is on errors of size up to three.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Cassuto, Y., Schwartz, M., Bohossian, V., Bruck, J.: Codes for asymmetric limited-magnitude errors with applications to multilevel flash memories. IEEE Trans. Inf. Theory 56(4), 1582–1595 (2010)

    Article  MathSciNet  Google Scholar 

  2. Chen, Z., Shparlinski, I.E., Winterhof, A.: Covering sets for limited-magnitude errors. IEEE Trans. Inf. Theory 60(9), 5315–5321 (2014)

    Article  MathSciNet  Google Scholar 

  3. Dickson, L.E.: History of the Theory of Numbers. Chelsea Publ, New York (1952)

    Google Scholar 

  4. Jiang, A., Langberg, M., Schwartz, M., Bruck, J.: Trajectory codes for flash memory. IEEE Trans. Inf. Theory 59(7), 4530–4541 (2013)

    Article  MathSciNet  Google Scholar 

  5. Kløve, T.: Two construction of covering sets for limited-magnitude errors, submitted for publication.

  6. Kløve, T., Bose, B., Elarief, N.: Systematic single limited magnitude error correcting codes for flash memories. IEEE Trans. Inf. Theory 57(7), 4477–4487 (2011)

    Article  MathSciNet  Google Scholar 

  7. Kløve, T., Luo, J., Naydenova, I., Yari, S.: Some codes correcting asymmetric errors of limited magnitude. IEEE Trans. Inf. Theory 57(11), 7459–7472 (2011)

    Article  MathSciNet  Google Scholar 

  8. Kløve, T., Luo, J., Yari, S.: Codes correcting single errors of limited magnitude. IEEE Trans. Inf. Theory 58, 2206–2219 (2012)

    Article  MathSciNet  Google Scholar 

  9. Kløve, T., Schwartz, M.: Covering sets for limited-magnitude errors. Preproceedings, International Workshop on Coding and Cryptography (WCC), 69-78, April 15-19, 2013, Bergen. http://www.selmer.uib.no/WCC2013/PreProceedings.pdf

  10. Kløve, T., Schwartz, M.: Linear covering codes and error-correcting codes for limited-magnitude errors, Designs. Codes Crypt. 73(2), 329–354 (2014)

    Article  MATH  Google Scholar 

  11. Kløve, T., Schwartz, M.: Erratum to: Linear covering codes and error-correcting codes for limited-magnitude errors, Designs. Codes Crypt. 73(3), 1029 (2014)

    Article  MATH  Google Scholar 

  12. The online encyclopedia of integer sequences. https://oeis.org

  13. Stein, S.K., Szabó, S.: Algebra and Tiling. The Mathematical Association of America (1994)

  14. Yari, S, Kløve, T., Bose, B.: Some codes correcting unbalanced errors of limited magnitude for flash memories. IEEE Trans. Inf. Theory 59(11), 7278–7287 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Torleiv Kløve.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kløve, T. On covering sets for limited-magnitude errors. Cryptogr. Commun. 8, 415–433 (2016). https://doi.org/10.1007/s12095-015-0154-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12095-015-0154-5

Keywords

Mathematics Subject Classification (2010)

Navigation