The Resource Advances in coding theory and crytography, editors T. Shaska ... [et al.], (electronic resource)

Advances in coding theory and crytography, editors T. Shaska ... [et al.], (electronic resource)

Label
Advances in coding theory and crytography
Title
Advances in coding theory and crytography
Statement of responsibility
editors T. Shaska ... [et al.]
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
In the new era of technology and advanced communications, coding theory and cryptography play a particularly significant role with a huge amount of research being done in both areas. This book presents some of that research, authored by prominent experts in the field.The book contains articles from a variety of topics most of which are from coding theory. Such topics include codes over order domains, Groebner representation of linear codes, Griesmer codes, optical orthogonal codes, lattices and theta functions related to codes, Goppa codes and Tschirnhausen modules, s-extremal codes, automorph
Member of
Cataloging source
MiAaPQ
Dewey number
  • 003.54
  • 003/.54
Illustrations
illustrations
Index
no index present
Language note
English
LC call number
QA268
LC item number
.A38 2007
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
  • (2007 :
  • (2007 :
http://library.link/vocab/relatedWorkOrContributorName
  • Shaska, Tanush
  • Conference in Coding Theory and Crytology
  • Applications of Computer Algebra Conference
Series statement
  • Series on coding theory and cryptology
  • Series on coding theory and cryptology
Series volume
  • v. 3
  • v. 3
http://library.link/vocab/subjectName
  • Coding theory
  • Cryptography
Label
Advances in coding theory and crytography, editors T. Shaska ... [et al.], (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
  • Preface; List of authors; CONTENTS; The key equation for codes from order domains J. B. Little; 1. Introduction; 2. Codes from Order Domains; 3. Preliminaries on Inverse Systems; 4. The Key Equation and its Relation to the BMS Algorithm; Acknowledgements; References; A Grobner representation for linear codes M. Borges-Quintana, M. A. Borges-Trenard and E. Mart nez-Moro; 1. Introduction; 2. M ̈oller's algorithm; 3. Gr ̈obner representation of a linear code; 4. Reduced and border bases; 4.1. Binary codes; 5. Applications; 5.1. Gradient decoding; 5.2. Permutation equivalent codes
  • 5.3. Gr ̈obner codewords for binary codesAcknowledgments; References; Arcs, minihypers, and the classification of three-dimensional Griesmer codes H. N. Ward; 1. Introduction; 2. Codes and the Griesmer bound; 3. Codes and multisets; 3.1. Arcs; 3.2. Combinations; 4. Minihypers; 4.1. The Hamada bound; 4.2. Achievement of the Griesmer bound; 5. Divisibility; 6. Three-dimensional Griesmer codes; 6.1. Orphans; 6.2. Divisibility; 6.3. The [92, 3, 80]8 codes; 6.4. Duality; Acknowledgment; References; Optical orthogonal codes from Singer groups T. L. Alderson and K. E. Mellinger; 1. Introduction
  • 2. Preliminaries 3. A construction from arcs in d-flats; 4. A construction from arcs of higher degree; 5. Affine constructions; 6. Conclusion; Acknowledgments; References; Codes over Fp 2 and Fp x Fp, lattices, and theta functions T. Shaska and C. Shor; 1. Introduction; 2. Preliminaries; 2.1. Theta functions over Fp; 3. Theta functions of codes over R; 3.1. A MacWilliams identity; 3.2. A generalization of the symmetric weight enumerator polynomial; 4. The injectivity of construction A; 4.1. The case p = 2; 4.2. The case p > 2; Acknowledgment; References
  • Goppa codes and Tschirnhausen modules D. Coles and E. PreviatoIntroduction; 1. Goppa Codes and rank-2 Vector Bundles; 2. The Klein Curve as Cover; 3. The Tschirnhausen Module of the Cover; 4. Goppa Codes and Adeles; 4.1. Adeles and pseudo-differentials; 4.2. Goppa codes and adeles; Acknowledgements; References; Remarks on s-extremal codes J.-L. Kim; 1. Introduction; 2. s-Extremal Additive F4 Codes; 3. s-Extremal Binary Codes; 4. Conclusion; Acknowledgments; References; Automorphism groups of generalized Reed-Solomon codes D. Joyner, A. Ksir and W. Traves; 1. Introduction
  • 2. AG codes and GRS codes 3. Automorphisms; 4. Examples; 5. Structure of the representations; References; About the code equivalence I. G. Bouyukliev; 1. Introduction; 2. Codes and binary matrices; 2.1. Equivalence of linear codes; 2.2. Isomorphism of binary matrices; 2.3. The connection between equivalence of linear codes and isomorphism of binary matrices; 3. Orbits, partitions, invariants; 3.1. Orbits; 3.2. Partitions, ordered partitions; 3.3. Definition of invariants; 3.4. Properties of partitions induced by invariants; 3.5. Invariants of columns and rows; 4. Main algorithm
  • 4.1. Additional invariants
Dimensions
unknown
Extent
1 online resource (268 p.)
Form of item
online
Isbn
9781281911896
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)1000000000410510
  • (EBL)1193247
  • (SSID)ssj0000288091
  • (PQKBManifestationID)12106010
  • (PQKBTitleCode)TC0000288091
  • (PQKBWorkID)10372360
  • (PQKB)11295799
  • (MiAaPQ)EBC1193247
  • (WSP)00006464
  • (EXLCZ)991000000000410510
Label
Advances in coding theory and crytography, editors T. Shaska ... [et al.], (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
  • Preface; List of authors; CONTENTS; The key equation for codes from order domains J. B. Little; 1. Introduction; 2. Codes from Order Domains; 3. Preliminaries on Inverse Systems; 4. The Key Equation and its Relation to the BMS Algorithm; Acknowledgements; References; A Grobner representation for linear codes M. Borges-Quintana, M. A. Borges-Trenard and E. Mart nez-Moro; 1. Introduction; 2. M ̈oller's algorithm; 3. Gr ̈obner representation of a linear code; 4. Reduced and border bases; 4.1. Binary codes; 5. Applications; 5.1. Gradient decoding; 5.2. Permutation equivalent codes
  • 5.3. Gr ̈obner codewords for binary codesAcknowledgments; References; Arcs, minihypers, and the classification of three-dimensional Griesmer codes H. N. Ward; 1. Introduction; 2. Codes and the Griesmer bound; 3. Codes and multisets; 3.1. Arcs; 3.2. Combinations; 4. Minihypers; 4.1. The Hamada bound; 4.2. Achievement of the Griesmer bound; 5. Divisibility; 6. Three-dimensional Griesmer codes; 6.1. Orphans; 6.2. Divisibility; 6.3. The [92, 3, 80]8 codes; 6.4. Duality; Acknowledgment; References; Optical orthogonal codes from Singer groups T. L. Alderson and K. E. Mellinger; 1. Introduction
  • 2. Preliminaries 3. A construction from arcs in d-flats; 4. A construction from arcs of higher degree; 5. Affine constructions; 6. Conclusion; Acknowledgments; References; Codes over Fp 2 and Fp x Fp, lattices, and theta functions T. Shaska and C. Shor; 1. Introduction; 2. Preliminaries; 2.1. Theta functions over Fp; 3. Theta functions of codes over R; 3.1. A MacWilliams identity; 3.2. A generalization of the symmetric weight enumerator polynomial; 4. The injectivity of construction A; 4.1. The case p = 2; 4.2. The case p > 2; Acknowledgment; References
  • Goppa codes and Tschirnhausen modules D. Coles and E. PreviatoIntroduction; 1. Goppa Codes and rank-2 Vector Bundles; 2. The Klein Curve as Cover; 3. The Tschirnhausen Module of the Cover; 4. Goppa Codes and Adeles; 4.1. Adeles and pseudo-differentials; 4.2. Goppa codes and adeles; Acknowledgements; References; Remarks on s-extremal codes J.-L. Kim; 1. Introduction; 2. s-Extremal Additive F4 Codes; 3. s-Extremal Binary Codes; 4. Conclusion; Acknowledgments; References; Automorphism groups of generalized Reed-Solomon codes D. Joyner, A. Ksir and W. Traves; 1. Introduction
  • 2. AG codes and GRS codes 3. Automorphisms; 4. Examples; 5. Structure of the representations; References; About the code equivalence I. G. Bouyukliev; 1. Introduction; 2. Codes and binary matrices; 2.1. Equivalence of linear codes; 2.2. Isomorphism of binary matrices; 2.3. The connection between equivalence of linear codes and isomorphism of binary matrices; 3. Orbits, partitions, invariants; 3.1. Orbits; 3.2. Partitions, ordered partitions; 3.3. Definition of invariants; 3.4. Properties of partitions induced by invariants; 3.5. Invariants of columns and rows; 4. Main algorithm
  • 4.1. Additional invariants
Dimensions
unknown
Extent
1 online resource (268 p.)
Form of item
online
Isbn
9781281911896
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)1000000000410510
  • (EBL)1193247
  • (SSID)ssj0000288091
  • (PQKBManifestationID)12106010
  • (PQKBTitleCode)TC0000288091
  • (PQKBWorkID)10372360
  • (PQKB)11295799
  • (MiAaPQ)EBC1193247
  • (WSP)00006464
  • (EXLCZ)991000000000410510

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