A Contribution to the Nonexistence of Perfect Codes PDF Download

Author: M. R. Best
Publisher:
ISBN:
Category : Coding theory
Languages : en
Pages : 118

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Author: Tuvi Etzion
Publisher: World Scientific
ISBN: 981125589X
Category : Mathematics
Languages : en
Pages : 436

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Book Description
In this monograph, we develop the theory of one of the most fascinating topics in coding theory, namely, perfect codes and related structures. Perfect codes are considered to be the most beautiful structure in coding theory, at least from the mathematical side. These codes are the largest ones with their given parameters. The book develops the theory of these codes in various metrics — Hamming, Johnson, Lee, Grassmann, as well as in other spaces and metrics. It also covers other related structures such as diameter perfect codes, quasi-perfect codes, mixed codes, tilings, combinatorial designs, and more. The goal is to give the aspects of all these codes, to derive bounds on their sizes, and present various constructions for these codes.The intention is to offer a different perspective for the area of perfect codes. For example, in many chapters there is a section devoted to diameter perfect codes. In these codes, anticodes are used instead of balls and these anticodes are related to intersecting families, an area that is part of extremal combinatorics. This is one example that shows how we direct our exposition in this book to both researchers in coding theory and mathematicians interested in combinatorics and extremal combinatorics. New perspectives for MDS codes, different from the classic ones, which lead to new directions of research on these codes are another example of how this book may appeal to both researchers in coding theory and mathematicians.The book can also be used as a textbook, either on basic course in combinatorial coding theory, or as an advance course in combinatorial coding theory.

Author: Isaac Woungang
Publisher: World Scientific
ISBN: 9812837175
Category : Computers
Languages : en
Pages : 725

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Book Description
Pt. 1. Applications of coding theory to computational complexity. ch. 1. Linear complexity and related complexity measures / Arne Winterhof. ch. 2. Lattice and construction of high coding gain lattices from codes / Mohammd-Reza Sadeghi. ch. 3. Distributed space-time codes with low ML decoding complexity / G. Susinder Rajan and B. Sundar Rajan -- pt. 2. Methods of algebraic combinatorics in coding theory/codes construction and existence. ch. 4. Coding theory and algebraic combinatorics / Michael Huber. ch. 5. Block codes from matrix and group rings / Paul Hurley and Ted Hurley. ch. 6. LDPC and convolutional codes from matrix and group rings / Paul Hurley and Ted Hurley. ch. 7. Search for good linear codes in the class of quasi-cyclic and related codes / Nuh Aydin and Tsvetan Asamov -- pt. 3. Source coding/channel capacity/network coding. ch. 8. Applications of universal source coding to statistical analysis of time series / Boris Ryabko. ch. 9. Introduction to network coding for acyclic and cyclic networks / Ángela I. Barbero and Øyvind Ytrehus. ch. 10. Distributed joint source-channel coding on a multiple access channel / Vinod Sharma and R. Rajesh -- pt. 4. Other selected topics in information and coding theory. ch. 11. Low-density parity-check codes and the related performance analysis methods / Xudong Ma. ch. 12. Variable length codes and finite automata / Marie-Pierre Béal [und weitere]. ch. 13. Decoding and finding the minimum distance with Gröbner Bases : history and new insights / Stanislav Bulygin and Ruud Pellikaan. ch. 14. Cooperative diversity systems for wireless communication / Murat Uysal and Muhammad Mehboob Fareed. ch. 15. Public key cryptography and coding theory / Pascal Véron

Author: Michal P. Chytil
Publisher: Springer Science & Business Media
ISBN: 9783540501107
Category : Computers
Languages : en
Pages : 582

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Book Description
This volume contains 11 invited lectures and 42 communications presented at the 13th Conference on Mathematical Foundations of Computer Science, MFCS '88, held at Carlsbad, Czechoslovakia, August 29 - September 2, 1988. Most of the papers present material from the following four fields: - complexity theory, in particular structural complexity, - concurrency and parellelism, - formal language theory, - semantics. Other areas treated in the proceedings include functional programming, inductive syntactical synthesis, unification algorithms, relational databases and incremental attribute evaluation.

Author: Ronald L. Graham
Publisher: Elsevier
ISBN: 9780444823465
Category : Business & Economics
Languages : en
Pages : 1124

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Book Description
Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.

Author: Demeter Krupka
Publisher: Elsevier
ISBN: 0080954235
Category : Mathematics
Languages : en
Pages : 787

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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: Christer Fernstrom
Publisher: Springer Science & Business Media
ISBN: 9783540164456
Category : Computers
Languages : en
Pages : 760

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Book Description
After historical introduction, the aspiration technique and imaging modalities are described. Thereafter, the use of aspiration cytology in the diagnosis and mainly in the sta- ging of urologic cancers is on still not well known appli- cations of the procedure in the staging of some organs (bladder, adrenals, penis, testis and secondary ureteral strictures) are reported.

Author: Jacobus H. van Lint
Publisher: Springer
ISBN: 3662207125
Category : Mathematics
Languages : en
Pages : 145

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Author: R.L. Graham
Publisher: Elsevier
ISBN: 008093384X
Category : Computers
Languages : en
Pages : 2404

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Handbook of Combinatorics

Author: M. Hall Jr.
Publisher: Springer Science & Business Media
ISBN: 940101826X
Category : Mathematics
Languages : en
Pages : 480

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Book Description
Combinatorics has come of age. It had its beginnings in a number of puzzles which have still not lost their charm. Among these are EULER'S problem of the 36 officers and the KONIGSBERG bridge problem, BACHET's problem of the weights, and the Reverend T.P. KIRKMAN'S problem of the schoolgirls. Many of the topics treated in ROUSE BALL'S Recreational Mathe matics belong to combinatorial theory. All of this has now changed. The solution of the puzzles has led to a large and sophisticated theory with many complex ramifications. And it seems probable that the four color problem will only be solved in terms of as yet undiscovered deep results in graph theory. Combinatorics and the theory of numbers have much in common. In both theories there are many prob lems which are easy to state in terms understandable by the layman, but whose solution depends on complicated and abstruse methods. And there are now interconnections between these theories in terms of which each enriches the other. Combinatorics includes a diversity of topics which do however have interrelations in superficially unexpected ways. The instructional lectures included in these proceedings have been divided into six major areas: 1. Theory of designs; 2. Graph theory; 3. Combinatorial group theory; 4. Finite geometry; 5. Foundations, partitions and combinatorial geometry; 6. Coding theory. They are designed to give an overview of the classical foundations of the subjects treated and also some indication of the present frontiers of research.