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
Subject
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1944-
http://library.link/vocab/creatorName
Niederreiter, Harald
Index
index present
LC call number
QA565
LC item number
.N594 2001
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1963-
http://library.link/vocab/relatedWorkOrContributorName
Xing, Chaoping
http://library.link/vocab/subjectName
  • Curves, Algebraic
  • Finite fields (Algebra)
  • Rational points (Geometry)
  • Coding theory
  • Courbes algébriques
  • Corps finis
  • Codage
  • Coding theory
  • Curves, Algebraic
  • Finite fields (Algebra)
  • Rational points (Geometry)
  • Eindige lichamen
  • Krommen
  • Corpos de classe
  • Teoria dos números
  • Criptologia
  • Computabilidade e complexidade
  • Courbes algébriques
  • Champs modulaires
Label
Rational points on curves over finite fields : theory and applications, Harald Niederreiter, Chaoping Xing
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 227-239) and index
Carrier category
volume
Carrier category code
  • nc
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
Dimensions
23 cm.
Extent
x, 245 pages
Isbn
9780521665438
Lccn
2001025570
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
System control number
  • (OCoLC)46402143
  • (OCoLC)ocm46402143
Label
Rational points on curves over finite fields : theory and applications, Harald Niederreiter, Chaoping Xing
Publication
Bibliography note
Includes bibliographical references (p. 227-239) and index
Carrier category
volume
Carrier category code
  • nc
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
Dimensions
23 cm.
Extent
x, 245 pages
Isbn
9780521665438
Lccn
2001025570
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
System control number
  • (OCoLC)46402143
  • (OCoLC)ocm46402143

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