1998 | OriginalPaper | Buchkapitel
Coding Theory
verfasst von : Rudolf Lidl, Günter Pilz
Erschienen in: Applied Abstract Algebra
Verlag: Springer New York
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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.