Lattices And Codes PDF Download
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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 | : 205 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3322900142 |
Download Lattices and Codes Book in PDF, ePub and Kindle
In the 2nd edition numerous corrections have been made. More basic material has been included to make the text even more self-contained. A new section on the automorphism group of the Leech lattice has been added. Some hints to new results have been incorporated. With several new exercises.
Author | : Wolfgang Ebeling |
Publisher | : Springer Science & Business Media |
Total Pages | : 178 |
Release | : 1994-01-01 |
Genre | : Coding theory |
ISBN | : 9783528064976 |
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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 | : 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 | : |
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Author | : Gabriele Nebe |
Publisher | : Springer Science & Business Media |
Total Pages | : 449 |
Release | : 2006-05-20 |
Genre | : Mathematics |
ISBN | : 3540307311 |
Download Self-Dual Codes and Invariant Theory Book in PDF, ePub and Kindle
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 | : Simeon Ball |
Publisher | : Springer Nature |
Total Pages | : 185 |
Release | : 2020-05-08 |
Genre | : Mathematics |
ISBN | : 3030411532 |
Download A Course in Algebraic Error-Correcting Codes Book in PDF, ePub and Kindle
This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.
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.