Coding Theory

  • Rudolf Lidl
  • Günter Pilz
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

In many ways, coding theory or the theory of error-correcting codes represents a beautiful example of the applicability of abstract algebra. Applications of codes range from enabling the clear transmission of pictures from distant planets to securing the enjoyment of listening to noise-free CDs. A variety of algebraic concepts can be used to describe codes and their properties, including matrices, polynomials and their roots, linear shift registers, and discrete Fourier transforms. The theory is still relatively young, having started in 1948 with an influential paper by Claude Shannon. This chapter provides the reader with an introduction to the basic concepts of (block) codes, beginning in §16 with general background, §17 deals with properties of linear codes, §18 introduces cyclic codes, and §19 and §20 contain material on special cyclic codes.

Keywords

Linear Code Cyclic Code Generator Polynomial Code Theory Perfect Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Rudolf Lidl
    • 1
  • Günter Pilz
    • 2
  1. 1.DVC OfficeUniversity of TasmaniaLauncestonAustria
  2. 2.Institut für MathematikUniversität LinzLinzAustria

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