Error-correcting codes and finite fields

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Clarendon Press, Oct 1, 1992 - Computers - 398 pages
This book provides the reader with all the tools necessary to implement modern error-processing techniques. 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 (but rigorous) treatment of the geometry of curves. The book is intended for the advanced instruction of engineers and computer scientists.

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Contents

Introduction
3
Linear codes
27
Definition of linear codes and fields Dimension and rate The generator
40
Copyright

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About the author (1992)

Sebastian Haffner was born in Berlin in 1907, and died in 1999. In 1938, he was forced to flee to Britain, where he worked as a journalist. In 1954, he returned to Germany and became a distinguished historian and commentator.
Oliver Pretzel, Sebastian Haffner's son, is the translator of this work.