This book provides the reader with all the tools necessary to implement modern error-processing schemes. It assumes only a basic knowledge of linear algebra and develops the mathematical theory in parallel with the codes. Central to the text are worked examples which motivate and explain the theory. The book is in four parts. The first introduces the basic ideas of coding theory. The second and third parts cover the theory of finite fields and give a detailed treatment of BCH and Reed Solomon codes. These parts are linked by their use of Euclid's algorithm as a central technique. The fourth part is devoted to Goppa codes, both classical and geometric, concluding with the Skorobogatov-Vladut error processor. A special feature of this part is a simplified treatment of the geometry of curves.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Illustrationen
line drawings, bibliography
ISBN-13
978-0-19-859678-3 (9780198596783)
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Schweitzer Klassifikation
Introduction; Block codes, weight, and distance; Linear codes; Error processing for linear codes; Hamming codes; Appendix: Linear algebra; Introduction and an example; Euclid's algorithm; Invertible and irreducible elements; The construction of finite fields; The structure of finite fields; Roots of polynomials; Primitive elements; Appendix: Polynomials over a field; BCH-codes as subcodes of Hamming codes; BCH codes as polynomial codes; Decoding BCH codes (1) the fundamental equation; Decoding BCH codes: (2) an error processing algorithm; Reed-Solomon codes and burst error correction; Bounds on codes; Classical Goppa codes; Classical Goppa codes: error processing; Introduction to algebraic curves; Functions on algebraic curves; A survey of the theory of algebraic curves; Geometric Goppa codes; An error processor for geometric Goppa codes.
