Lattices And Codes PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lattices And Codes PDF full book. Access full book title Lattices And Codes.
| Author | : Wolfgang Ebeling |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 177 |
| Release | : 2013 |
| Genre | : Computers |
| ISBN | : 3658003596 |
Download Lattices and Codes Book in PDF, ePub and Kindle
The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory. In the 3rd edition, again numerous corrections and improvements have been made and the text has been updated. Content Lattices and Codes -Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes. Readership Graduate Students in Mathematics and Computer Science Mathematicians and Computer Scientists About the Author Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, Leibniz Universität Hannover, Germany
| Author | : Wolfgang Ebeling |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 191 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 3322968790 |
Download Lattices and Codes Book in PDF, ePub and Kindle
The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory.Das Ziel der Codierungstheorie ist der Entwurf eines effektiven Transformierungssystems für Informationen. Die mathematische Behandlung führt zu bestimmten endlichen Strukturen: fehlerkorrigierende Codes. Überraschenderweise stellt sich heraus, daß Zusammenhänge, die für den Entwurf solcher Codes interessant sind, eng mit Problemen, die zuvor und unabhängig davon in der Reinen Mathematik studiert wurden, verwandt sind. Dieses Buch handelt von einem Beispiel für eine solche Verwandtschaft: die von Codes und Gittern. Gitter werden in der Zahlentheorie und in der Zahlengeometrie studiert. Viele Probleme in bezug auf Codes haben ihr Gegenstück in Gittern und Kugelpackungen.
| Author | : Sueli I.R. Costa |
| Publisher | : Springer |
| Total Pages | : 123 |
| Release | : 2018-04-02 |
| Genre | : Mathematics |
| ISBN | : 3319678825 |
Download Lattices Applied to Coding for Reliable and Secure Communications Book in PDF, ePub and Kindle
This book provides a first course on lattices – mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields.
| Author | : Wolfgang Ebeling |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 178 |
| Release | : 1994-01-01 |
| Genre | : Coding theory |
| ISBN | : 9783528064976 |
Download Lattices and Codes Book in PDF, ePub and Kindle
| Author | : Ram Zamir |
| Publisher | : Cambridge University Press |
| Total Pages | : 459 |
| Release | : 2014-08-07 |
| Genre | : Technology & Engineering |
| ISBN | : 1139991590 |
Download Lattice Coding for Signals and Networks Book in PDF, ePub and Kindle
Unifying information theory and digital communication through the language of lattice codes, this book provides a detailed overview for students, researchers and industry practitioners. It covers classical work by leading researchers in the field of lattice codes and complementary work on dithered quantization and infinite constellations, and then introduces the more recent results on 'algebraic binning' for side-information problems, and linear/lattice codes for networks. It shows how high dimensional lattice codes can close the gap to the optimal information theoretic solution, including the characterisation of error exponents. The solutions presented are based on lattice codes, and are therefore close to practical implementations, with many advanced setups and techniques, such as shaping, entropy-coding, side-information and multi-terminal systems. Moreover, some of the network setups shown demonstrate how lattice codes are potentially more efficient than traditional random-coding solutions, for instance when generalising the framework to Gaussian networks.
| Author | : J.H. Conway |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 724 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475722494 |
Download Sphere Packings, Lattices and Groups Book in PDF, ePub and Kindle
The second edition of this timely, 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 continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries.
| Author | : Ishai Haviv |
| Publisher | : |
| Total Pages | : 109 |
| Release | : 2011 |
| Genre | : |
| ISBN | : |
Download Lattices and Codes Book in PDF, ePub and Kindle
| Author | : John Conway |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 778 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475765681 |
Download Sphere Packings, Lattices and Groups Book in PDF, ePub and Kindle
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 | : Minjia Shi |
| Publisher | : World Scientific |
| Total Pages | : 232 |
| Release | : 2019-11-20 |
| Genre | : Mathematics |
| ISBN | : 9811212937 |
Download Codes And Modular Forms: A Dictionary Book in PDF, ePub and Kindle
There are connections between invariant theory and modular forms since the times of Felix Klein, in the 19th century, connections between codes and lattices since the 1960's. The aim of the book is to explore the interplay between codes and modular forms. Here modular form is understood in a wide sense (Jacobi forms, Siegel forms, Hilbert forms). Codes comprises not only linear spaces over finite fields but modules over some commutative rings. The connection between codes over finite fields and lattices has been well documented since the 1970s. Due to an avalanche of results on codes over rings since the 1990's there is a need for an update at book level.
| Author | : J. H. van Lint |
| Publisher | : Springer |
| Total Pages | : 146 |
| Release | : 2009-08-14 |
| Genre | : Mathematics |
| ISBN | : 3540366571 |
Download Coding Theory Book in PDF, ePub and Kindle
These lecture notes are the contents of a two-term course given by me during the 1970-1971 academic year as Morgan Ward visiting professor at the California Institute of Technology. The students who took the course were mathematics seniors and graduate students. Therefore a thorough knowledge of algebra. (a. o. linear algebra, theory of finite fields, characters of abelian groups) and also probability theory were assumed. After introducing coding theory and linear codes these notes concern topics mostly from algebraic coding theory. The practical side of the subject, e. g. circuitry, is not included. Some topics which one would like to include 1n a course for students of mathematics such as bounds on the information rate of codes and many connections between combinatorial mathematics and coding theory could not be treated due to lack of time. For an extension of the course into a third term these two topics would have been chosen. Although the material for this course came from many sources there are three which contributed heavily and which were used as suggested reading material for the students. These are W. W. Peterson's Error-Correcting Codes «(15]), E. R. Berlekamp's Algebraic Coding Theory «(5]) and several of the AFCRL-reports by E. F. Assmus, H. F. Mattson and R. Turyn ([2], (3), [4] a. o. ). For several fruitful discussions I would like to thank R. J. McEliece.
