Algebraic function fields and codes by Henning Stichtenoth

Cover of: Algebraic function fields and codes | Henning Stichtenoth

Published by Springer-Verlag in London .

Written in English

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Edition Notes

Book details

StatementHenning Stichtenoth.
The Physical Object
Paginationx,260p.
Number of Pages260
ID Numbers
Open LibraryOL15275607M
ISBN 103540564896

Download Algebraic function fields and codes

15 years after the?rst printing of Algebraic Function Fields and Codes,the mathematics editors of Springer Verlag encouraged me to revise and extend the book. Besides numerous minor corrections and amendments, the second edition di?ers from the?rst one in two respects.

Firstly I have included a. Since aboutfunction 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.

Algebraic Function Fields and Codes (Graduate Texts in Mathematics Book ) - Kindle edition by Henning Stichtenoth. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Algebraic Function Fields and Codes (Graduate Texts in Mathematics Book ).5/5(1).

Aug 22,  · Since aboutfunction 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 5/5(1).

Review of the book "Algebraic Function Fields and Codes (2nd Edition)" by Henning Stichtenoth Springer, ISBN: Steven Galbraith Department of Mathematics, The University of Auckland, New Zealand June 17, 1 Summary of the review Algebraic geometry is a major branch of mathematics and the theory of curves over nite elds.

Jun 25,  · Algebraic Function Fields and Codes book. Read reviews from world’s largest community for readers. This book links two subjects: algebraic geometry and c /5(4).

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. 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. Nov 20,  · 15 years after the?rst printing of Algebraic Function Fields and Codes,the mathematics editors of Springer Verlag encouraged me to revise and extend the book.

Besides numerous minor corrections and amendments, the second edition di?ers from the?rst one in two respects. Firstly I have included a series of exercises at the end of each chapter.

Description: The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes aroundmany applications of function fields were found in different areas of mathematics and information theory.

Function fields arising from varieties, curves and Riemann surfaces. The function field of an algebraic variety of dimension n over k is an algebraic function field of n variables over k. Two varieties are birationally equivalent if and only if their function fields are isomorphic.

Nov 18,  · This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes/5(4).

Jan 27,  · An algebraic function field in one variable, over a given field K, is an extension of K of transcendence degree one. These field extensions are naturally associated to algebraic curves over the given field and as such have been studied in algebraic geometry since the 19 th century.

On the other hand, when the ground field K is a finite field, the arithmetic of a function field in one variable. Since aboutfunction 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 ekodeniz.com by: introduction to coding theory and algebraic geometry Download introduction to coding theory and algebraic geometry or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get introduction to coding theory and algebraic geometry book now. This site is like a library, Use search box in the widget to get. For algebraic background and more detailed proofs of algebraic facts, I think a great book is "Algebraic Function Fields and Codes" by Stichtenoth.

The first chapter of it covers up most of the algebraic background needed, without any special prerequisites (you may want to have some fimiliarity with definitions from ring theory but not more.

Algebraic geometry codes: basic notions / Michael Tsfasman, Serge Vladut, Dmitry Nogin. Function Fields and Algebraic Curves Historical and Bibliographic Notes The main interests of the authors of this book lie where algebraic geometry meets number theory.

This leads to a point of view on coding theory different from. Buy Algebraic Function Fields and Codes (Universitext) by Henning Stichtenoth (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible ekodeniz.coms: 1. Jun 17,  · Get Now ekodeniz.com?book=Reads Read Book Algebraic Function Fields and Codes (Graduate Texts in Mathematics) E-Book Free New E-Books.

Henning Stichtenoth is the author of Algebraic Function Fields and Codes ( avg rating, 4 ratings, 0 reviews, published ), Algebraic Function Fiel /5(4). In this correspondence, we present new linear codes over F8 and F9 based on the construction by Xing and Niederreiter using algebraic function fields and places of small.

In this chapter we introduce the basic definitions and results of the theory of algebraic function fields: valuations, places, divisors, the genus of a function field, adeles, Weil differentials.

Goppa codes, which can be viewed as a generalization of BCH codes, get around this problem. Finding long Goppa codes reduces the problem of finding algebraic curves with many rational points. We will see that, for any algebraic curve over a finite field, there is an analogue of the Riemann Zeta function.

Thus far we have encountered very few explicit examples of algebraic function fields, namely the rational function field K(x)/K (cf.

Section ) and some quadratic extensions of the rational function field (Example ). Now we would like to discuss some other examples in detail. From May 30 to June 3,the University of North Carolina at Greensboro will host the UNCG Summer School in Computational Number Theory: Function Fields.

The speakers will be. I am studying Riemann-Roch theorem on the book by Stitchtenoth, "Algebraic function fields and codes". I am having some troubles understanding a exact sequence of linear mappings between Riemann-Roch.

Sep 21,  · The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes aroundmany applications of function fields were found in different areas of mathematics and information theory.

This book presents survey articles on some of these new developments. Algebraic Function Fields In large parts of this book, the basic theory of algebraic function fields is assumed. In this appendix we collect the main definitions, notations and results of this theory.

For a detailed exposition the reader is referred to the books “Al-gebraic Function Fields and Codes” by H. Stichtenoth (Springer Universitext. Buy a cheap copy of Algebraic Curves over Finite Fields: book by Carlos Moreno.

In this tract, Professor Moreno develops the theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of Free shipping over $ Jul 02,  · Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes.

The book is the natural continuation of Algebraic Geometric. Through a set of related yet distinct texts, the author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions: Ideal- and valuation-theoretic aspects, L functions and class field theory, together with a presentation of algebraic foundations which are usually undersized in standard algebra courses.

Providing a modern, self-contained exposition of the theory of Algebraic function fields, this work introduces VD Goppa's Algebraic-geometric ekodeniz.com also includes a decoding algorithm for these codes as well as a discussion of their subfield subcodes and trace codes.

Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory.

For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. ThisBrand: Springer-Verlag New York.

Oct 11,  · Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codesPrice: $ Sep 01,  · The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics.

On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc.

Algebraic curves, that is, algebraic varieties of dimension 1, are crucial for the applications that will be discussed in Chapters 5 and 6.

In the present chapter, we emphasize the interplay between algebraic curves and function fields, which has become a powerful tool in both the theory and the applications. Diophantine geometry and, more generally, arithmetic geometry is the study of the points of an algebraic variety with coordinates in fields that are not algebraically closed and occur in algebraic number theory, such as the field of rational numbers, number fields, finite fields, function fields, and p-adic fields.

May 04,  · The book lacks the quantity of examples and exercises one might want from a textbook, and there are other books that cover much of the same material (Stichtenoth's Algebraic Function Fields and Codes is a particular favorite of this reviewer, for example).

That said, I have found myself reaching for Niederreiter and Xing's book several times in. Differentials of Algebraic Function Fields.- Algebraic Function Fields over Finite Constant Fields.- Examples of Algebraic Function Fields.- Asymptotic Bounds for the Number of Rational Places.- More about Algebraic Geometry Codes.- Subfield Subcodes and Trace Codes.

Reviews. From the reviews of the second edition: "In this book we have an. An algebraic function field over K is an algebraic extension of finite degree over the rational function field K(x) (the ground field K may be an arbitrary field).

This type of field extension occurs naturally in various branches of mathematics such as algebraic geometry, number theory and the theory of compact Riemann surfaces. Kopparty S () Review of algebraic function fields and codes by Henning Stichtenoth, ACM SIGACT News,(), Online publication date: Jun Chen H Efficient compromising resilient authentication schemes for large scale wireless sensor networks Proceedings of the third ACM conference on Wireless network security, ().Jan 11,  · Do you want to remove all your recent searches?

All recent searches will be deleted.The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes aroundmany applications of function fields were found in different areas of mathematics and information theory.

This book presents survey articles on some of these new developments.

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