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Algebraic Function Fields and Codes

2009-02-11 Mathematics
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Release : 2009-02-11
Genre : Mathematics
Kind : eBook
Book Rating : 785/5 ( reviews)

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Book Synopsis Algebraic Function Fields and Codes by : Henning Stichtenoth

Download or read book Algebraic Function Fields and Codes written by Henning Stichtenoth. This book was released on 2009-02-11. Available in PDF, EPUB and Kindle. Book excerpt: 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. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.

Algebraic Function Fields and Codes

2008-11-20 Mathematics
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Release : 2008-11-20
Genre : Mathematics
Kind : eBook
Book Rating : 777/5 ( reviews)

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Book Synopsis Algebraic Function Fields and Codes by : Henning Stichtenoth

Download or read book Algebraic Function Fields and Codes written by Henning Stichtenoth. This book was released on 2008-11-20. Available in PDF, EPUB and Kindle. Book excerpt: 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. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.

Algebraic Function

1993 Mathematics
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Release : 1993
Genre : Mathematics
Kind : eBook
Book Rating : 898/5 ( reviews)

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Book Synopsis Algebraic Function by : Henning Stichtenoth

Download or read book Algebraic Function written by Henning Stichtenoth. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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.

Topics in the Theory of Algebraic Function Fields

2007-10-10 Mathematics
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Release : 2007-10-10
Genre : Mathematics
Kind : eBook
Book Rating : 152/5 ( reviews)

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Book Synopsis Topics in the Theory of Algebraic Function Fields by : Gabriel Daniel Villa Salvador

Download or read book Topics in the Theory of Algebraic Function Fields written by Gabriel Daniel Villa Salvador. This book was released on 2007-10-10. Available in PDF, EPUB and Kindle. Book excerpt: The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.

Number Theory in Function Fields

2013-04-18 Mathematics
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Release : 2013-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 469/5 ( reviews)

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Book Synopsis Number Theory in Function Fields by : Michael Rosen

Download or read book Number Theory in Function Fields written by Michael Rosen. This book was released on 2013-04-18. Available in PDF, EPUB and Kindle. Book excerpt: Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.

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