Coverart for item
The Resource Rational points on curves over finite fields : theory and applications, Harald Niederreiter, Chaoping Xing

Rational points on curves over finite fields : theory and applications, Harald Niederreiter, Chaoping Xing

Label
Rational points on curves over finite fields : theory and applications
Title
Rational points on curves over finite fields
Title remainder
theory and applications
Statement of responsibility
Harald Niederreiter, Chaoping Xing
Creator
Contributor
Author
Subject
Language
eng
Summary
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
Member of
Cataloging source
UkCbUP
http://library.link/vocab/creatorDate
1944-
http://library.link/vocab/creatorName
Niederreiter, Harald
Dewey number
516.3/52
Index
index present
LC call number
QA565
LC item number
.N594 2001
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorDate
1963-
http://library.link/vocab/relatedWorkOrContributorName
Xing, Chaoping
Series statement
London Mathematical Society lecture note series
Series volume
285
http://library.link/vocab/subjectName
  • Curves, Algebraic
  • Finite fields (Algebra)
  • Rational points (Geometry)
  • Coding theory
Label
Rational points on curves over finite fields : theory and applications, Harald Niederreiter, Chaoping Xing
Instantiates
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Local Fields
  • Newton Polygons
  • Ramification Groups and Conductors
  • Global Fields
  • Ray Class Fields and Hilbert Class Fields
  • Narrow Ray Class Fields
  • Class Field Towers
  • Explicit Function Fields
  • Kummer and Artin-Schreier Extensions
  • Cyclotomic Function Fields
  • Background on Function Fields
  • Drinfeld Modules of Rank 1
  • Function Fields with Many Rational Places
  • Function Fields from Hilbert Class Fields
  • Function Fields from Narrow Ray Class Fields
  • The First Construction
  • The Second Construction
  • The Third Construction
  • Function Fields from Cyclotomic Fields
  • Explicit Function Fields
  • Asymptotic Results
  • Riemann-Roch Theorem
  • Asymptotic Behavior of Towers
  • The Lower Bound of Serre
  • Further Lower Bounds for A(q[superscript m])
  • Explicit Towers
  • Lower Bounds on A(2), A(3), and A(5)
  • Applications to Algebraic Coding Theory
  • Goppa's Algebraic-Geometry Codes
  • Beating the Asymptotic Gilbert-Varshamov Bound
  • NXL Codes
  • XNL Codes
  • Divisor Class Groups and Ideal Class Groups
  • A Propagation Rule for Linear Codes
  • Applications to Cryptography
  • Background on Stream Ciphers and Linear Complexity
  • Constructions of Almost Perfect Sequences
  • A Construction of Perfect Hash Families
  • Hash Families and Authentication Schemes
  • Applications to Low-Discrepancy Sequences
  • Algebraic Extensions and the Hurwitz Formula
  • Ramification Theory of Galois Extensions
  • Constant Field Extensions
  • Zeta Functions and Rational Places
  • Class Field Theory
Control code
CR9781107325951
Extent
1 online resource (x, 245 pages)
Form of item
online
Isbn
9780521665438
Isbn Type
(paperback)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote
Label
Rational points on curves over finite fields : theory and applications, Harald Niederreiter, Chaoping Xing
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Local Fields
  • Newton Polygons
  • Ramification Groups and Conductors
  • Global Fields
  • Ray Class Fields and Hilbert Class Fields
  • Narrow Ray Class Fields
  • Class Field Towers
  • Explicit Function Fields
  • Kummer and Artin-Schreier Extensions
  • Cyclotomic Function Fields
  • Background on Function Fields
  • Drinfeld Modules of Rank 1
  • Function Fields with Many Rational Places
  • Function Fields from Hilbert Class Fields
  • Function Fields from Narrow Ray Class Fields
  • The First Construction
  • The Second Construction
  • The Third Construction
  • Function Fields from Cyclotomic Fields
  • Explicit Function Fields
  • Asymptotic Results
  • Riemann-Roch Theorem
  • Asymptotic Behavior of Towers
  • The Lower Bound of Serre
  • Further Lower Bounds for A(q[superscript m])
  • Explicit Towers
  • Lower Bounds on A(2), A(3), and A(5)
  • Applications to Algebraic Coding Theory
  • Goppa's Algebraic-Geometry Codes
  • Beating the Asymptotic Gilbert-Varshamov Bound
  • NXL Codes
  • XNL Codes
  • Divisor Class Groups and Ideal Class Groups
  • A Propagation Rule for Linear Codes
  • Applications to Cryptography
  • Background on Stream Ciphers and Linear Complexity
  • Constructions of Almost Perfect Sequences
  • A Construction of Perfect Hash Families
  • Hash Families and Authentication Schemes
  • Applications to Low-Discrepancy Sequences
  • Algebraic Extensions and the Hurwitz Formula
  • Ramification Theory of Galois Extensions
  • Constant Field Extensions
  • Zeta Functions and Rational Places
  • Class Field Theory
Control code
CR9781107325951
Extent
1 online resource (x, 245 pages)
Form of item
online
Isbn
9780521665438
Isbn Type
(paperback)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote

Library Locations

Processing Feedback ...