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| Author | : Michele Elia |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2004 |
| Genre | : |
| ISBN | : |
| Author | : Alexander Barg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 317 |
| Release | : 2001 |
| Genre | : Computers |
| ISBN | : 0821820745 |
This volume presents papers related to the DIMACS workshop, "Codes and Association Schemes". The articles are devoted to the following topics: applications of association schemes and of the polynomial method to properties of codes, structural results for codes, structural results for association schemes, and properties of orthogonal polynomials and their applications in combinatorics. Papers on coding theory are related to classical topics, such as perfect codes, bounds on codes, codes and combinatorial arrays, weight enumerators, and spherical designs. Papers on orthogonal polynomials provide new results on zeros and symptotic properties of standard families of polynomials encountered in coding theory. The theme of association schemes is represented by new classification results and new classes of schemes related to posets. This volume collects up-to-date applications of the theory of association schemes to coding and presents new properties of both polynomial and general association schemes. It offers a solid representation of results in problems in areas of current interest.
| Author | : |
| Publisher | : |
| Total Pages | : 484 |
| Release | : 2004 |
| Genre | : Combinatorial analysis |
| ISBN | : |
| Author | : T. Ericson |
| Publisher | : Elsevier |
| Total Pages | : 565 |
| Release | : 2001-04-27 |
| Genre | : Mathematics |
| ISBN | : 0080502164 |
Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. Mathematically the topic belongs to the realm of algebraic combinatorics, with close connections to number theory, geometry, combinatorial theory, and - of course - to algebraic coding theory. The connections to physics occur within areas like crystallography and nuclear physics. In engineering spherical codes are of central importance in connection with error-control in communication systems. In that context the use of spherical codes is often referred to as "coded modulation." The book offers a first complete treatment of the mathematical theory of codes on Euclidean spheres. Many new results are published here for the first time. Engineering applications are emphasized throughout the text. The theory is illustrated by many examples. The book also contains an extensive table of best known spherical codes in dimensions 3-24, including exact constructions.
| Author | : J. J. Seidel |
| Publisher | : Academic Press |
| Total Pages | : 431 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483268004 |
Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.
| Author | : Eiichi Bannai |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 303 |
| Release | : 2021-02-22 |
| Genre | : Mathematics |
| ISBN | : 3110627736 |
This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.
| Author | : John H. Conway |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 690 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475720165 |
The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today.
| Author | : Eiichi Bannai |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 444 |
| Release | : 2021-02-22 |
| Genre | : Mathematics |
| ISBN | : 3110630257 |
Algebraic combinatorics is the study of combinatorial objects as an extension of the study of finite permutation groups, or, in other words, group theory without groups. In the spirit of Delsarte's theory, this book studies combinatorial objects such as graphs, codes, designs, etc. in the general framework of association schemes, providing a comprehensive overview of the theory as well as pointing out to extensions.
| Author | : John Conway |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 778 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475765681 |
The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.
| Author | : Chris Godsil |
| Publisher | : CRC Press |
| Total Pages | : 382 |
| Release | : 1993-04-01 |
| Genre | : Mathematics |
| ISBN | : 9780412041310 |
This book presents an introduction to some of the interactions between algebra and combinatorics. It focuses on the characteristic and matchings polynomials of a graph and introduces the theory of polynomial spaces. The book is intended for beginning graduate students in mathematics.
