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Error Correcting Codes

  • David R. Finston
  • Patrick J. Morandi
Chapter
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)

Abstract

The identification number schemes we discussed in the previous chapter give us the ability to determine if an error has been made in recording or transmitting information. However, they are limited in two ways. First, the types of errors detected are fairly restrictive, e.g. single digit errors or interchanging digits. Second, they provide no way to recover the intended information. Some more sophisticated ideas and mathematical concepts enable methods to encoding and transmit information in ways that allow both detection and correction of errors. There are many applications of these so-called error correcting codes, among them transmission of digital images from planetary probes and playing compact discs and DVD movies.

Supplementary material

978-3-319-04498-9_2_MOESM1_ESM.mw (47 kb)
Cosets (MW 47 KB)

References

  1. 1.
    Hankerson DC et al (2000) Coding theory and cryptography: the essentials, 2nd edn. Marcel Dekker, New YorkCrossRefGoogle Scholar
  2. 2.
    Herstein I (1975) Topics in algebra, 2nd edn. Wiley, HobokenzbMATHGoogle Scholar
  3. 3.
    Talbot J, Welsh D (2006) Complexity and cryptography: an introduction. Cambridge University Press, CambridgeCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • David R. Finston
    • 1
    • 2
  • Patrick J. Morandi
    • 3
  1. 1.Department of MathematicsBrooklyn College of the City University of New YorkBrooklynUSA
  2. 2.CUNY Graduate CenterNew YorkUSA
  3. 3.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

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