Rational Points on Curves over Finite Fields
Subtitle: Theory and Applications (London Mathematical Society Lecture Note Series)
Publisher: Cambridge University Press
Published: June 18, 2001
Language: eng
Format: Paperback
Number of pages: 256
ISBN-13: 9780521665438
Subjects: Algebra; Science/Mathematics; General; Algebraic Geometry; Theory Of Groups; Mathematics; Rational points (Geometry); Geometry - Algebraic; Algebra - General; Mathematics / Algebra / General; Group Theory; Coding theory; Curves, Algebraic; Finite fields (Algebra)
First sentence: Some basic definitions and fundamental properties of algebraic function fields are introduced in this chapter.
Description: Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.