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Cyclic Codes

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

Abstract

In this chapter we will build codes from quotient rings of \(\mathbb{Z}_{2}[x]\). One advantage of this construction will be that we can guarantee a certain degree of error correction. We first make a connection between words and elements of such a quotient ring.

Supplementary material

978-3-319-04498-9_7_MOESM1_ESM.mw (46 kb)
Section-7.4-Exercise-3 (MW 46 KB)

References

  1. 1.
    Hankerson D et al (2000) Coding theory and cryptography: the essentials, 2nd edn. Marcel Dekker, New YorkCrossRefGoogle Scholar
  2. 2.
    van der Waerden BL (1971) Modern algebra. Springer, BerlinGoogle 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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