Algebraic Curves and Finite Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Curves and Finite Fields write by Harald Niederreiter. This book was released on 2014-08-20. Algebraic Curves and Finite Fields available in PDF, EPUB and Kindle. Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples. This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.
Algebraic Curves over a Finite Field
Algebraic Curves over a Finite Field - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Curves over a Finite Field write by J. W. P. Hirschfeld. This book was released on 2013-03-25. Algebraic Curves over a Finite Field available 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.
Algebraic Curves Over Finite Fields
Algebraic Curves Over Finite Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Curves Over Finite Fields write by Carlos Moreno. This book was released on 1993-10-14. Algebraic Curves Over Finite Fields available 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.
Codes on Algebraic Curves
Codes on Algebraic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Codes on Algebraic Curves write by Serguei A. Stepanov. This book was released on 1999-07-31. Codes on Algebraic Curves available in PDF, EPUB and Kindle. This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.
Algebraic Geometry and Its Applications
Algebraic Geometry and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry and Its Applications write by Jean Chaumine. This book was released on 2008. Algebraic Geometry and Its Applications available in PDF, EPUB and Kindle. This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.
