The Resource Advances in algebraic geometry codes, editors, Edgar Martinez-Moro, Carlos Munuera, Diego Ruano, (electronic resource)

Advances in algebraic geometry codes, editors, Edgar Martinez-Moro, Carlos Munuera, Diego Ruano, (electronic resource)

Label
Advances in algebraic geometry codes
Title
Advances in algebraic geometry codes
Statement of responsibility
editors, Edgar Martinez-Moro, Carlos Munuera, Diego Ruano
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned rese
Member of
Cataloging source
MiAaPQ
Dewey number
  • 005.7/2
  • 005.72
  • 516.35
Illustrations
illustrations
Index
no index present
Language note
English
LC call number
QA268
LC item number
.A378 2008
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Martinez-Moro, Edgar
  • Munera, Carlos
  • Ruano, Diego
Series statement
Series on coding theory and cryptology,
Series volume
v. 5
http://library.link/vocab/subjectName
  • Coding theory
  • Geometry, Algebraic
  • Error-correcting codes (Information theory)
Label
Advances in algebraic geometry codes, editors, Edgar Martinez-Moro, Carlos Munuera, Diego Ruano, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • Contents; Preface; 1. Algebraic Geometry Codes: General Theory I.M. Duursma; Contents; Introduction; 1.1 Linear codes and the a ne line; 1.1.1 Dimension and in nite families; 1.1.2 Duality and di erentials; 1.1.3 Minimum distance; 1.1.4 Error correction; 1.1.5 Linear secret sharing schemes; 1.1.6 Weight distributions and codes over extension elds; 1.2. Cyclic codes and classical Goppa codes; 1.2.1. Reed-Solomon and BCH codes; 1.2.2. Classical Goppa codes; 1.2.3. Dual BCH codes; 1.3. Reed-Muller codes; 1.4. Geometric Goppa codes; 1.4.1. Curves and linear codes
  • 1.4.2. Duality and differentials1.4.3. Families of curves; 1.4.4. One-point codes; 1.4.5. Two-point codes; 1.4.6. Error correction; 1.4.7. Secret reconstruction for algebraic-geometric LSSSs; 1.4.8. Weight distributions; 1.5. Bibliographic notes; References; 2. The Decoding of Algebraic Geometry Codes P. Beelen and T. H holdt; Contents; 2.1. Introduction; 2.2. The basic algorithm; 2.2.1. Decoding; 2.2.2. The basic algorithm for decoding of algebraic geome- try codes; 2.3. Syndrome formulation of the basic algorithm; 2.4. The generalized order bound; 2.5. Majority voting
  • 2.6. List decoding of algebraic geometry codes2.7. Syndrome formulation of list decoding; 2.8. Literature; References; 3. The Key Equation for One-Point Codes M.E. O'Sullivan and M. Bras-Amor os; Contents; 3.1. Introduction; 3.2. The key equation for Reed-Solomon codes; 3.2.1. Reed-Solomon codes; 3.2.2. Polynomials for decoding; 3.2.3. The key equation and the Berlekamp-Massey algorithm; 3.2.4. Error evaluation without the evaluator polynomial; 3.2.5. Connections to the Euclidean algorithm; 3.3. The key equation for Hermitian codes; 3.3.1. The Hermitian curve; 3.3.2. Hermitian codes
  • 3.3.3. Polynomials for decoding3.3.4. Another basis for Fq2(x; y); 3.3.5. The key equation; 3.3.6. Solving the key equation; 3.3.7. Error evaluation without the error evalua- tor polynomials; 3.3.8. An example; 3.4. The key equation for one-point codes; 3.4.1. Curves, function fields and differentials; 3.4.2. One-point codes and their duals; 3.4.3. The trace and a dual basis; 3.4.4. Polynomials for decoding; 3.4.5. The key equation and its solution; 3.4.6. Error evaluation without the error evaluator polynomials; 3.5. Bibliographical notes; References
  • 4. Evaluation Codes from an Affine Variety Code Perspective O. Geil4.1. Introduction; 4.2. Affine variety codes; 4.3. Some Grobner basis theoretical tools; 4.4. A bound on the minimum distance of C(I; L); 4.5. The Feng-Rao bound for C(I; L)?; 4.6. Using weighted degree orderings; 4.7. The order domain conditions; 4.8. Weight functions and order domains; 4.9. Codes form order domains; 4.10. One-point geometric Goppa codes; 4.11. Bibliographical Notes; References; 5. Asymptotically Good Codes H. Niederreiter and F. Ozbudak; Contents; 5.1. Introduction; 5.2. Preliminaries
  • 5.3. Two Constructions of Asymptotically Good Codes
Dimensions
unknown
Extent
1 online resource (453 p.)
Form of item
online
Isbn
9789812794017
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)1000000000765737
  • (EBL)1193246
  • (SSID)ssj0000572868
  • (PQKBManifestationID)12159027
  • (PQKBTitleCode)TC0000572868
  • (PQKBWorkID)10529879
  • (PQKB)10677601
  • (MiAaPQ)EBC1193246
  • (WSP)00002147
  • (EXLCZ)991000000000765737
Label
Advances in algebraic geometry codes, editors, Edgar Martinez-Moro, Carlos Munuera, Diego Ruano, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • Contents; Preface; 1. Algebraic Geometry Codes: General Theory I.M. Duursma; Contents; Introduction; 1.1 Linear codes and the a ne line; 1.1.1 Dimension and in nite families; 1.1.2 Duality and di erentials; 1.1.3 Minimum distance; 1.1.4 Error correction; 1.1.5 Linear secret sharing schemes; 1.1.6 Weight distributions and codes over extension elds; 1.2. Cyclic codes and classical Goppa codes; 1.2.1. Reed-Solomon and BCH codes; 1.2.2. Classical Goppa codes; 1.2.3. Dual BCH codes; 1.3. Reed-Muller codes; 1.4. Geometric Goppa codes; 1.4.1. Curves and linear codes
  • 1.4.2. Duality and differentials1.4.3. Families of curves; 1.4.4. One-point codes; 1.4.5. Two-point codes; 1.4.6. Error correction; 1.4.7. Secret reconstruction for algebraic-geometric LSSSs; 1.4.8. Weight distributions; 1.5. Bibliographic notes; References; 2. The Decoding of Algebraic Geometry Codes P. Beelen and T. H holdt; Contents; 2.1. Introduction; 2.2. The basic algorithm; 2.2.1. Decoding; 2.2.2. The basic algorithm for decoding of algebraic geome- try codes; 2.3. Syndrome formulation of the basic algorithm; 2.4. The generalized order bound; 2.5. Majority voting
  • 2.6. List decoding of algebraic geometry codes2.7. Syndrome formulation of list decoding; 2.8. Literature; References; 3. The Key Equation for One-Point Codes M.E. O'Sullivan and M. Bras-Amor os; Contents; 3.1. Introduction; 3.2. The key equation for Reed-Solomon codes; 3.2.1. Reed-Solomon codes; 3.2.2. Polynomials for decoding; 3.2.3. The key equation and the Berlekamp-Massey algorithm; 3.2.4. Error evaluation without the evaluator polynomial; 3.2.5. Connections to the Euclidean algorithm; 3.3. The key equation for Hermitian codes; 3.3.1. The Hermitian curve; 3.3.2. Hermitian codes
  • 3.3.3. Polynomials for decoding3.3.4. Another basis for Fq2(x; y); 3.3.5. The key equation; 3.3.6. Solving the key equation; 3.3.7. Error evaluation without the error evalua- tor polynomials; 3.3.8. An example; 3.4. The key equation for one-point codes; 3.4.1. Curves, function fields and differentials; 3.4.2. One-point codes and their duals; 3.4.3. The trace and a dual basis; 3.4.4. Polynomials for decoding; 3.4.5. The key equation and its solution; 3.4.6. Error evaluation without the error evaluator polynomials; 3.5. Bibliographical notes; References
  • 4. Evaluation Codes from an Affine Variety Code Perspective O. Geil4.1. Introduction; 4.2. Affine variety codes; 4.3. Some Grobner basis theoretical tools; 4.4. A bound on the minimum distance of C(I; L); 4.5. The Feng-Rao bound for C(I; L)?; 4.6. Using weighted degree orderings; 4.7. The order domain conditions; 4.8. Weight functions and order domains; 4.9. Codes form order domains; 4.10. One-point geometric Goppa codes; 4.11. Bibliographical Notes; References; 5. Asymptotically Good Codes H. Niederreiter and F. Ozbudak; Contents; 5.1. Introduction; 5.2. Preliminaries
  • 5.3. Two Constructions of Asymptotically Good Codes
Dimensions
unknown
Extent
1 online resource (453 p.)
Form of item
online
Isbn
9789812794017
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)1000000000765737
  • (EBL)1193246
  • (SSID)ssj0000572868
  • (PQKBManifestationID)12159027
  • (PQKBTitleCode)TC0000572868
  • (PQKBWorkID)10529879
  • (PQKB)10677601
  • (MiAaPQ)EBC1193246
  • (WSP)00002147
  • (EXLCZ)991000000000765737

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