Self-Dual Codes and Invariant Theory

Self-Dual Codes and Invariant Theory

Author: Gabriele Nebe

Publisher: Springer Science & Business Media

Published: 2006-05-20

Total Pages: 449

ISBN-13: 3540307311

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One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory, which has inspired hundreds of papers about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.


Book Synopsis Self-Dual Codes and Invariant Theory by : Gabriele Nebe

Download or read book Self-Dual Codes and Invariant Theory written by Gabriele Nebe and published by Springer Science & Business Media. This book was released on 2006-05-20 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory, which has inspired hundreds of papers about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.

Self-Dual Codes and Invariant Theory

Self-Dual Codes and Invariant Theory

Author: Gabriele Nebe

Publisher: Springer Science & Business Media

Published: 2006-02-09

Total Pages: 474

ISBN-13: 9783540307297

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One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory, which has inspired hundreds of papers about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.


Book Synopsis Self-Dual Codes and Invariant Theory by : Gabriele Nebe

Download or read book Self-Dual Codes and Invariant Theory written by Gabriele Nebe and published by Springer Science & Business Media. This book was released on 2006-02-09 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory, which has inspired hundreds of papers about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.

Algebraic Informatics

Algebraic Informatics

Author: Symeon Bozapalidis

Publisher: Springer Science & Business Media

Published: 2009-08-28

Total Pages: 370

ISBN-13: 3642035639

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This book constitutes the refereed proceedings of the Third International Conference on Algebraic Informatics, CAI 2009, held in Thessaloniki, Greece, in May 2009. The 16 full papers were carefully reviewed and selected from 25 submissions. The papers cover topics such as algebraic semantics on graph and trees, formal power series, syntactic objects, algebraic picture processing, finite and infinite computations, acceptors and transducers for strings, trees, graphs arrays, etc. decision problems, algebraic characterization of logical theories, process algebra, algebraic algorithms, algebraic coding theory, algebraic aspects of cryptography.


Book Synopsis Algebraic Informatics by : Symeon Bozapalidis

Download or read book Algebraic Informatics written by Symeon Bozapalidis and published by Springer Science & Business Media. This book was released on 2009-08-28 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Algebraic Informatics, CAI 2009, held in Thessaloniki, Greece, in May 2009. The 16 full papers were carefully reviewed and selected from 25 submissions. The papers cover topics such as algebraic semantics on graph and trees, formal power series, syntactic objects, algebraic picture processing, finite and infinite computations, acceptors and transducers for strings, trees, graphs arrays, etc. decision problems, algebraic characterization of logical theories, process algebra, algebraic algorithms, algebraic coding theory, algebraic aspects of cryptography.

Introduction to Global Variational Geometry

Introduction to Global Variational Geometry

Author: Demeter Krupka

Publisher: Elsevier

Published: 2000-04-01

Total Pages: 787

ISBN-13: 0080954235

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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures- New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity- Basic structures and tools: global analysis, smooth manifolds, fibred spaces


Book Synopsis Introduction to Global Variational Geometry by : Demeter Krupka

Download or read book Introduction to Global Variational Geometry written by Demeter Krupka and published by Elsevier. This book was released on 2000-04-01 with total page 787 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures- New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity- Basic structures and tools: global analysis, smooth manifolds, fibred spaces

Computational Invariant Theory

Computational Invariant Theory

Author: Harm Derksen

Publisher: Springer

Published: 2015-12-23

Total Pages: 366

ISBN-13: 3662484226

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This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.


Book Synopsis Computational Invariant Theory by : Harm Derksen

Download or read book Computational Invariant Theory written by Harm Derksen and published by Springer. This book was released on 2015-12-23 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.

Algebraic Aspects of Digital Communications

Algebraic Aspects of Digital Communications

Author: Tanush Shaska

Publisher: IOS Press

Published: 2009

Total Pages: 296

ISBN-13: 1607500191

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-Proceedings of the NATO Advanced Study Institute on New Challenges in Digital Communications, Vlora, Albania, 27 April - 9 May 2008.---T.p. verso.


Book Synopsis Algebraic Aspects of Digital Communications by : Tanush Shaska

Download or read book Algebraic Aspects of Digital Communications written by Tanush Shaska and published by IOS Press. This book was released on 2009 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: -Proceedings of the NATO Advanced Study Institute on New Challenges in Digital Communications, Vlora, Albania, 27 April - 9 May 2008.---T.p. verso.

Algorithms in Invariant Theory

Algorithms in Invariant Theory

Author: Bernd Sturmfels

Publisher: Springer Science & Business Media

Published: 2008-06-17

Total Pages: 202

ISBN-13: 3211774173

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This book is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to research ideas, hints for applications, outlines and details of algorithms, examples and problems.


Book Synopsis Algorithms in Invariant Theory by : Bernd Sturmfels

Download or read book Algorithms in Invariant Theory written by Bernd Sturmfels and published by Springer Science & Business Media. This book was released on 2008-06-17 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to research ideas, hints for applications, outlines and details of algorithms, examples and problems.

Code Based Secret Sharing Schemes: Applied Combinatorial Coding Theory

Code Based Secret Sharing Schemes: Applied Combinatorial Coding Theory

Author: Patrick Sole

Publisher: World Scientific

Published: 2022-04-11

Total Pages: 215

ISBN-13: 9811248346

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Secret sharing schemes form one of the most important topic in Cryptography. These protocols are used in many areas, applied mathematics, computer science, electrical engineering. A secret is divided into several pieces called shares. Each share is given to a user of the system. Each user has no information about the secret, but the secret can be retrieved by certain authorized coalition of users.This book is devoted to such schemes inspired by Coding Theory. The classical schemes of Shamir, Blakley, Massey are recalled. Survey is made of research in Combinatorial Coding Theory they triggered, mostly self-dual codes, and minimal codes. Applications to engineering like image processing, and key management of MANETs are highlighted.


Book Synopsis Code Based Secret Sharing Schemes: Applied Combinatorial Coding Theory by : Patrick Sole

Download or read book Code Based Secret Sharing Schemes: Applied Combinatorial Coding Theory written by Patrick Sole and published by World Scientific. This book was released on 2022-04-11 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Secret sharing schemes form one of the most important topic in Cryptography. These protocols are used in many areas, applied mathematics, computer science, electrical engineering. A secret is divided into several pieces called shares. Each share is given to a user of the system. Each user has no information about the secret, but the secret can be retrieved by certain authorized coalition of users.This book is devoted to such schemes inspired by Coding Theory. The classical schemes of Shamir, Blakley, Massey are recalled. Survey is made of research in Combinatorial Coding Theory they triggered, mostly self-dual codes, and minimal codes. Applications to engineering like image processing, and key management of MANETs are highlighted.

Algebra and Coding Theory

Algebra and Coding Theory

Author: A. Leroy

Publisher: American Mathematical Society

Published: 2023-05-01

Total Pages: 270

ISBN-13: 147046859X

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This volume contains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, in honor of Tariq Rizvi, held from July 5–7, 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held on July 8, 2021, both of which were hosted by the Université d'Artois, Lens, France. The articles cover topics in commutative and noncommutative algebra and applications to coding theory. In some papers, applications of Frobenius rings, the skew group rings, and iterated Ore extensions to coding theory are discussed. Other papers discuss classical topics, such as Utumi rings, Baer rings, nil and nilpotent algebras, and Brauer groups. Still other articles are devoted to various aspects of the elementwise study for rings and modules. Lastly, this volume includes papers dealing with questions in homological algebra and lattice theory. The articles in this volume show the vivacity of the research of noncommutative rings and its influence on other subjects.


Book Synopsis Algebra and Coding Theory by : A. Leroy

Download or read book Algebra and Coding Theory written by A. Leroy and published by American Mathematical Society. This book was released on 2023-05-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, in honor of Tariq Rizvi, held from July 5–7, 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held on July 8, 2021, both of which were hosted by the Université d'Artois, Lens, France. The articles cover topics in commutative and noncommutative algebra and applications to coding theory. In some papers, applications of Frobenius rings, the skew group rings, and iterated Ore extensions to coding theory are discussed. Other papers discuss classical topics, such as Utumi rings, Baer rings, nil and nilpotent algebras, and Brauer groups. Still other articles are devoted to various aspects of the elementwise study for rings and modules. Lastly, this volume includes papers dealing with questions in homological algebra and lattice theory. The articles in this volume show the vivacity of the research of noncommutative rings and its influence on other subjects.

Cryptography and Coding

Cryptography and Coding

Author: Maura B. Paterson

Publisher: Springer Nature

Published: 2021-12-14

Total Pages: 323

ISBN-13: 3030926419

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This book constitutes the refereed proceedings of the 18th IMA International Conference on Cryptography and Coding, IMACC 2021, held in December 2021. Due to COVID 19 pandemic the conference was held virtually. The 14 papers presented were carefully reviewed and selected from 30 submissions. The conference focuses on a diverse set of topics both in cryptography and coding theory.


Book Synopsis Cryptography and Coding by : Maura B. Paterson

Download or read book Cryptography and Coding written by Maura B. Paterson and published by Springer Nature. This book was released on 2021-12-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 18th IMA International Conference on Cryptography and Coding, IMACC 2021, held in December 2021. Due to COVID 19 pandemic the conference was held virtually. The 14 papers presented were carefully reviewed and selected from 30 submissions. The conference focuses on a diverse set of topics both in cryptography and coding theory.