Algebraic Function Fields And Codes PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Algebraic Function Fields And Codes PDF full book. Access full book title Algebraic Function Fields And Codes.
| Author | : Henning Stichtenoth |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 360 |
| Release | : 2009-02-11 |
| Genre | : Mathematics |
| ISBN | : 3540768785 |
Download Algebraic Function Fields and Codes Book in PDF, ePub and Kindle
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.
| Author | : Gabriel Daniel Villa Salvador |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 658 |
| Release | : 2007-10-10 |
| Genre | : Mathematics |
| ISBN | : 0817645152 |
Download Topics in the Theory of Algebraic Function Fields Book in PDF, ePub and Kindle
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.
| Author | : Michael Rosen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 355 |
| Release | : 2013-04-18 |
| Genre | : Mathematics |
| ISBN | : 1475760469 |
Download Number Theory in Function Fields Book in PDF, ePub and Kindle
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.
| Author | : Harald Niederreiter |
| Publisher | : Princeton University Press |
| Total Pages | : 272 |
| Release | : 2009-09-21 |
| Genre | : Mathematics |
| ISBN | : 140083130X |
Download Algebraic Geometry in Coding Theory and Cryptography Book in PDF, ePub and Kindle
This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory 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 codes Features applications to cryptography not treated in other books
| Author | : David Goldschmidt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 195 |
| Release | : 2006-04-06 |
| Genre | : Mathematics |
| ISBN | : 0387224459 |
Download Algebraic Functions and Projective Curves Book in PDF, ePub and Kindle
This book gives an introduction to algebraic functions and projective curves. It covers a wide range of material by dispensing with the machinery of algebraic geometry and proceeding directly via valuation theory to the main results on function fields. It also develops the theory of singular curves by studying maps to projective space, including topics such as Weierstrass points in characteristic p, and the Gorenstein relations for singularities of plane curves.
| Author | : J. W. P. Hirschfeld |
| Publisher | : Princeton University Press |
| Total Pages | : 717 |
| Release | : 2013-03-25 |
| Genre | : Mathematics |
| ISBN | : 1400847419 |
Download Algebraic Curves over a Finite Field Book in PDF, ePub and Kindle
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
| Author | : Emil Artin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 366 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821840754 |
Download Algebraic Numbers and Algebraic Functions Book in PDF, ePub and Kindle
Originated from the notes of a course given at Princeton University in 1950-1951, this text offers an introduction to algebraic numbers and algebraic functions. It starts with the general theory of valuation fields, proceeds to the local class field theory, and then to the theory of function fields in one variable.
| Author | : David Goss |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642614809 |
Download Basic Structures of Function Field Arithmetic Book in PDF, ePub and Kindle
From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062
| Author | : Carlos Moreno |
| Publisher | : Cambridge University Press |
| Total Pages | : 264 |
| Release | : 1993-10-14 |
| Genre | : Mathematics |
| ISBN | : 9780521459013 |
Download Algebraic Curves Over Finite Fields Book in PDF, ePub and Kindle
Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.
| Author | : Claude Chevalley |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 204 |
| Release | : 1951-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821815067 |
Download Introduction to the Theory of Algebraic Functions of One Variable Book in PDF, ePub and Kindle
Presents an approach to algebraic geometry of curves that is treated as the theory of algebraic functions on the curve. This book discusses such topics as the theory of divisors on a curve, the Riemann-Roch theorem, $p$-adic completion, and extensions of the fields of functions (covering theory) and of the fields of constants.
