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Codes on Algebraic Curves

Authors: Stepanov, Serguei A.

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eBook 166,59 €
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  • ISBN 978-1-4615-4785-3
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Hardcover 207,95 €
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  • ISBN 978-0-306-46144-6
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Softcover 207,95 €
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  • ISBN 978-1-4613-7167-0
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About this book

This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.

Table of contents (13 chapters)

Buy this book

eBook 166,59 €
price for Spain (gross)
  • ISBN 978-1-4615-4785-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 207,95 €
price for Spain (gross)
  • ISBN 978-0-306-46144-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 207,95 €
price for Spain (gross)
  • ISBN 978-1-4613-7167-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Codes on Algebraic Curves
Authors
Copyright
1999
Publisher
Springer US
Copyright Holder
Kluwer Academic/Plenum Publishers
eBook ISBN
978-1-4615-4785-3
DOI
10.1007/978-1-4615-4785-3
Hardcover ISBN
978-0-306-46144-6
Softcover ISBN
978-1-4613-7167-0
Edition Number
1
Number of Pages
XIII, 350
Topics