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Algebraic Function Fields and Codes (Graduate Texts in Mathematics) Paperback – November 19, 2010

ISBN-13: 978-3642095566 ISBN-10: 3642095569 Edition: Softcover reprint of hardcover 2nd ed. 2008
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Editorial Reviews

Review

From the reviews of the second edition:

"In this book we have an exposition of the theory of function fields in one variable from the algebraic point of view … . The book is carefully written, the concepts are well motivated and plenty of examples help to understand the ideas and proofs and so it can be used as a textbook for an introductory course on the (classical) arithmetic of function fields with an application to coding theory." (Felipe Zaldivar, MAA Online, January, 2009)

From the Back Cover

The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields.

This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Other exercises are more advanced and cover additional material which could not be included in the text.

This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering.

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Product Details

  • Series: Graduate Texts in Mathematics (Book 254)
  • Paperback: 360 pages
  • Publisher: Springer; Softcover reprint of hardcover 2nd ed. 2008 edition (November 19, 2010)
  • Language: English
  • ISBN-10: 3642095569
  • ISBN-13: 978-3642095566
  • Product Dimensions: 6.1 x 0.8 x 9.2 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #3,020,535 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

5 of 5 people found the following review helpful By Mathieu Dutour on August 22, 2003
Format: Paperback
Coding theory is fundamental to make digital transmission technology work efficiently and usually uses Reed-Solomon codes. The "natural" extension of those codes is to consider riemann surfaces over finite fields.
The theory is developped from scratch and does not assume any knowledge of algebraic geometry. The author gave a proof of the Hasse-Weil bounds using the Zeta function. In parallel the theory of linear codes and Goppa codes is introduced from the beginning.
While the author do not consider the geometry of riemann surfaces, having a knowledge of riemann surfaces over C can help a lot.
This short book should be considered as a very nice introduction to geometric goppa codes.
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Algebraic Function Fields and Codes (Graduate Texts in Mathematics)
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