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Item Details
| Title:
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ALGEBRAIC FUNCTION
FIELDS AND CODES |
| By: |
Henning Stichtenoth |
| Format: |
Paperback |
| List price:
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£27.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3540564896 |
| ISBN 13: |
9783540564898 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
25 June, 1993 |
| Series: |
Universitext |
| Pages: |
270 |
| Description: |
Providing a modern, self-contained exposition of the theory of algebraic function fields, this work introduces VD Goppa's algebraic-geometric codes. It also includes a decoding algorithm for these codes as well as a discussion of their subfield subcodes and trace codes. It is useful to students in algebraic geometry and coding theory. |
| Synopsis: |
This book has two objectives. The first is to fill a void in the existing mathematical literature by providing a modern, self-contained and in-depth exposition of the theory of algebraic function fields. The topics include the Riemann-Roch theorem, algebraic extensions of function fields, ramifications theory and differentials. Particular emphasis is placed on function fields over a finite constant field, leading into zeta functions and the Hasse-Weil theorem. Numerous examples illustrate the general theory. Error-correcting codes are in widespread use for the reliable transmission of information. Perhaps the most fascinating of all the ties that link the theory of these codes to mathematics is the construction by V.D. Goppa, of powerful codes using techniques borrowed from algebraic geometry. Algebraic function fields provide the most elementary approach to Goppa's ideas, and the second objective of this book is to provide an introduction to Goppa's algebraic-geometric codes along these lines. The codes, their parameters and links with traditional codes such as classical Goppa, Peed-Solomon and BCH codes are treated at an early stage of the book.Subsequent chapters include a decoding algorithm for these codes as well as a discussion of their subfield subcodes and trace codes. Stichtenoth's book will be very useful to students and researchers in algebraic geometry and coding theory and to computer scientists and engineers interested in information transmission. |
| Illustrations: |
7 illus. |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Returnable |
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