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
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The item Rational points on curves over finite fields : theory and applications, Harald Niederreiter, Chaoping Xing represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Rational points on curves over finite fields : theory and applications, Harald Niederreiter, Chaoping Xing represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 Ever since the seminal work of Goppa on algebraicgeometry 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 lowdiscrepancy 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 lowdiscrepancy sequences
 Language
 eng
 Extent
 1 online resource (x, 245 pages)
 Note
 Title from publisher's bibliographic system (viewed on 05 Oct 2015)
 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 ArtinSchreier 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
 RiemannRoch 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 AlgebraicGeometry Codes
 Beating the Asymptotic GilbertVarshamov 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 LowDiscrepancy Sequences
 Algebraic Extensions and the Hurwitz Formula
 Ramification Theory of Galois Extensions
 Constant Field Extensions
 Zeta Functions and Rational Places
 Class Field Theory
 Isbn
 9780521665438
 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
 Language
 eng
 Summary
 Ever since the seminal work of Goppa on algebraicgeometry 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 lowdiscrepancy 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 lowdiscrepancy sequences
 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
 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 ArtinSchreier 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
 RiemannRoch 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 AlgebraicGeometry Codes
 Beating the Asymptotic GilbertVarshamov 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 LowDiscrepancy 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
 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 ArtinSchreier 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
 RiemannRoch 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 AlgebraicGeometry Codes
 Beating the Asymptotic GilbertVarshamov 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 LowDiscrepancy 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
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Rationalpointsoncurvesoverfinitefields/sW2PMKtKRVI/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Rationalpointsoncurvesoverfinitefields/sW2PMKtKRVI/">Rational points on curves over finite fields : theory and applications, Harald Niederreiter, Chaoping Xing</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>