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Algebra and Applications

Topics in Geometry, Coding Theory and Cryptography

Editors: Garcia, Arnaldo, Stichtenoth, Henning (Eds.)

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About this book

The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory, such as coding theory, sphere packings and lattices, sequence design, and cryptography. The use of function fields often led to better results than those of classical approaches.

This book presents survey articles on some of these new developments. Most of the material is directly related to the interaction between function fields and their various applications; in particular the structure and the number of rational places of function fields are of great significance. The topics focus on material which has not yet been presented in other books or survey articles. Wherever applications are pointed out, a special effort has been made to present some background concerning their use.

Reviews

From the reviews:

"This book contains five surveys on different topic related to coding theory. The chapters are largely independent from each other and one can browse freely through them. ... The book is well-written and I think it may be valuable both for researchers and for students with background in algebra. ... In fact, the main interest of this book is that it focuses on topics not covered in other books on coding theory." (Fabio Mainardi, MAA Online, January, 2007)


Table of contents (5 chapters)

Table of contents (5 chapters)
  • EXPLICIT TOWERS OF FUNCTION FIELDS OVER FINITE FIELDS

    Pages 1-58

    Garcia, Arnaldo (et al.)

  • FUNCTION FIELDS OVER FINITE FIELDS AND THEIR APPLICATIONS TO CRYPTOGRAPHY

    Pages 59-104

    Niederreiter, Harald (et al.)

  • ARTIN-SCHREIER EXTENSIONS AND THEIR APPLICATIONS

    Pages 105-133

    Güneri, Cem (et al.)

  • PSEUDORANDOM SEQUENCES

    Pages 135-166

    Topuzoğlu, Alev (et al.)

  • GROUP STRUCTURE OF ELLIPTIC CURVES OVER FINITE FIELDS AND APPLICATIONS

    Pages 167-194

    Murty, Ram (et al.)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-1-4020-5334-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-1-4020-5333-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
Softcover $139.00
price for USA in USD
  • ISBN 978-90-481-7345-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topics in Geometry, Coding Theory and Cryptography
Editors
  • Arnaldo Garcia
  • Henning Stichtenoth
Series Title
Algebra and Applications
Series Volume
6
Copyright
2007
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-5334-4
DOI
10.1007/1-4020-5334-4
Hardcover ISBN
978-1-4020-5333-7
Softcover ISBN
978-90-481-7345-7
Series ISSN
1572-5553
Edition Number
1
Number of Pages
X, 201
Topics

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