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Author: Gabriele Nebe Publisher: Springer Science & Business Media ISBN: 3540307311 Category : Mathematics Languages : en Pages : 449
Book Description
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.
Author: Gabriele Nebe Publisher: Springer Science & Business Media ISBN: 3540307311 Category : Mathematics Languages : en Pages : 449
Book Description
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.
Author: Gabriele Nebe Publisher: Springer Science & Business Media ISBN: 9783540307297 Category : Mathematics Languages : en Pages : 474
Book Description
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.
Author: Symeon Bozapalidis Publisher: Springer Science & Business Media ISBN: 3642035639 Category : Computers Languages : en Pages : 370
Book Description
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.
Author: Demeter Krupka Publisher: Elsevier ISBN: 0080954235 Category : Mathematics Languages : en Pages : 787
Book Description
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
Author: Harm Derksen Publisher: Springer ISBN: 3662484226 Category : Mathematics Languages : en Pages : 366
Book Description
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.
Author: Tanush Shaska Publisher: IOS Press ISBN: 1607500191 Category : Computers Languages : en Pages : 296
Book Description
-Proceedings of the NATO Advanced Study Institute on New Challenges in Digital Communications, Vlora, Albania, 27 April - 9 May 2008.---T.p. verso.
Author: Harm Derksen Publisher: Springer Science & Business Media ISBN: 3662049589 Category : Mathematics Languages : en Pages : 272
Book Description
This book, the first volume of a subseries on "Invariant Theory and Algebraic Transformation Groups", provides a comprehensive and up-to-date overview of the algorithmic aspects of invariant theory. Numerous illustrative examples and a careful selection of proofs make the book accessible to non-specialists.
Author: Bernd Sturmfels Publisher: Springer Science & Business Media ISBN: 3211774173 Category : Mathematics Languages : en Pages : 202
Book Description
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.
Author: Patrick Sole Publisher: World Scientific ISBN: 9811248346 Category : Computers Languages : en Pages : 215
Book Description
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.
Author: A. Leroy Publisher: American Mathematical Society ISBN: 147046859X Category : Mathematics Languages : en Pages : 270
Book Description
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.
Author: Gabriele Nebe
Author: Gabriele Nebe
Author: Gabriele Nebe
Author: Symeon Bozapalidis
Author: Demeter Krupka
Author: Harm Derksen
Author: Tanush Shaska
Author: Harm Derksen
Author: Bernd Sturmfels
Author: Patrick Sole
Author: A. Leroy