Skip to main content

A new double error correcting long code for 100% correction

  • Conference paper
Thinkquest~2010

Abstract

The theory of Linear Block codes is well established since many years. Shannon’s work (1948) showed that at any rate of information transmission up to the channel capacity, it should be possible to transfer information at error rates that can be reduced to any desired level [1]. In 1950, Hamming introduced a single error correcting and double error detecting codes with its geometrical model [2] whereas just before Hamming, Golay had introduced (23, 12) triple error correcting perfect code. Since then different types of more effective error correcting codes have been invented by researchers.

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 159.00
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

  1. Shannon C. E., “Mathematical theory of communication”, Bell Sys. Tech. Journal. 27, 1948, pp 379-423 and 623-656

    Google Scholar 

  2. Hamming, R.W.,”Error Detecting and Error Correcting Codes”, The Bell System Technical Journal,Soc, Industrial. Appl. Math. Vol. 26, No.2, April 1950

    Google Scholar 

  3. J. H. Van Lint “On the nonexistence of perfect 2- and 3- Hamming-error-correcting-codes over GF(q)”, IEEE Transaction on Information and Control, Vol. 16, No. 4, June 1970

    Google Scholar 

  4. S. G. S. SHIVA, K. C. FUNG and H. S. Y. TAN, “On Permutation Decoding of Binary Cyclic Double- Error-Correcting Codes of Certain Lengths” IEEE Transaction on Information Theory, Sept 1970, pp 641-643

    Google Scholar 

  5. C. L. CHENZ “Computer Results on the Minimum Distance of Some with Binary Cyclic Codes” IEEE Transaction on Information Theory, may 1970, Vol. IT-18, pp 359-360

    Google Scholar 

  6. James massey “A short introduction to coding theory and practice” Proceeding of International symposium on signal, system and electronics, Germany, Sept 89, pp 629- 633

    Google Scholar 

  7. A E Brouwer, Tom Verhoeff, “An Updated table of minimum distance bounds for binary linear code “, IEEE Transaction on Information Theory, Vol. 39. No. 2, march 93, pp 662-677

    Google Scholar 

  8. T. Aaron Gulliver and Vijay K. Bhargava, “A Systematic (16,8) Code for Correcting Double Errors and Detecting Triple Adjacent Errors” IEEE Transaction on Computers, Vol. 42, No. 1, Jan 1993, pp. 109-112

    Article  Google Scholar 

  9. S. Lin and D.J. Costello, Error Control Coding: fundamentals and applications, Prentice Hall, 1983

    Google Scholar 

  10. S.B. Wicker, Error Control Systems for Digital Communication and Storage, Prentice Hall, 1994

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer India Pvt. Ltd

About this paper

Cite this paper

Gomes, J., Mishra, B. (2011). A new double error correcting long code for 100% correction. In: Pise, S.J. (eds) Thinkquest~2010. Springer, New Delhi. https://doi.org/10.1007/978-81-8489-989-4_47

Download citation

  • DOI: https://doi.org/10.1007/978-81-8489-989-4_47

  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-8489-988-7

  • Online ISBN: 978-81-8489-989-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics