Skip to main content
SpringerLink
Log in

Codes of Length 2 Correcting Single Errors of Limited Size

  • Conference paper
  • First Online:
Cryptography and Coding (IMACC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9496))

Included in the following conference series:

Abstract

Linear codes over \(\mathbb {Z}_q\) of length 2, correcting single errors of size at most \(k\), are considered. It is determined for which q such codes exists and explicit code constructions are given for those q. One case remains open, namely \(q=(k+1)(k+2)\), where \(k+1\) is a prime power. For this case we conjecture that no such codes exist.

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

Access this chapter

Log in via an institution
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 EPUB and 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

Institutional subscriptions

References

  1. Elarief, N., Bose, B.: Optimal, systematic, \(q\)-ary codes correcting all asymmetric and symmetric errors of limited magnitude. IEEE Trans. Inf. Theory 56, 979–983 (2010)

    Article  MathSciNet  Google Scholar 

  2. Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers, 4th edn. Oxford University Press, London (1962)

    MATH  Google Scholar 

  3. Jiang, A., Mateescu, R., Schwartz, M., Bruck, J.: Rank modulation for flash memories. IEEE Trans. Inf. Theory 55, 2659–2673 (2009)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. 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 

  6. Schwartz, M.: Quasi-cross lattice tilings with applications to flash memory. IEEE Trans. Inf. Theory 58, 2397–2405 (2012)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Bergen, 5020, Bergen, Norway

    Torleiv Kløve

Authors
  1. Torleiv Kløve
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Torleiv Kløve .

Editor information

Editors and Affiliations

  1. University College London, Cambridge, United Kingdom

    Jens Groth

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kløve, T. (2015). Codes of Length 2 Correcting Single Errors of Limited Size. In: Groth, J. (eds) Cryptography and Coding. IMACC 2015. Lecture Notes in Computer Science(), vol 9496. Springer, Cham. https://doi.org/10.1007/978-3-319-27239-9_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27239-9_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27238-2

  • Online ISBN: 978-3-319-27239-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation