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Introduction to Coding Theory by J.H. van Lint (English) Hardcover Book

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Specificaties

Objectstaat
Nieuw: Een nieuw, ongelezen en ongebruikt boek in perfecte staat waarin geen bladzijden ontbreken of ...
ISBN-13
9783540641339
Book Title
Introduction to Coding Theory
ISBN
9783540641339
Publication Name
Introduction to Coding Theory
Item Length
9.3in
Publisher
Springer Berlin / Heidelberg
Series
Graduate Texts in Mathematics Ser.
Publication Year
1998
Type
Textbook
Format
Hardcover
Language
English
Item Height
0.3in
Author
J. H. Van Lint
Item Width
6.1in
Item Weight
19.3 Oz
Number of Pages
Xiv, 234 Pages

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Product Information

It is gratifying that this textbook is still sufficiently popular to warrant a third edition. I have used the opportunity to improve and enlarge the book. When the second edition was prepared, only two pages on algebraic geometry codes were added. These have now been removed and replaced by a relatively long chapter on this subject. Although it is still only an introduction, the chapter requires more mathematical background of the reader than the remainder of this book. One of the very interesting recent developments concerns binary codes defined by using codes over the alphabet 7l.4* There is so much interest in this area that a chapter on the essentials was added. Knowledge of this chapter will allow the reader to study recent literature on 7l. -codes. 4 Furthermore, some material has been added that appeared in my Springer Lec­ ture Notes 201, but was not included in earlier editions of this book, e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller Codes. In Chapter 2, a section on "Coding Gain" ( the engineer's justification for using error-correcting codes) was added. For the author, preparing this third edition was a most welcome return to mathematics after seven years of administration. For valuable discussions on the new material, I thank C.P.l.M.Baggen, I. M.Duursma, H.D.L.Hollmann, H. C. A. van Tilborg, and R. M. Wilson. A special word of thanks to R. A. Pellikaan for his assistance with Chapter 10.

Product Identifiers

Publisher
Springer Berlin / Heidelberg
ISBN-10
3540641335
ISBN-13
9783540641339
eBay Product ID (ePID)
122071

Product Key Features

Author
J. H. Van Lint
Publication Name
Introduction to Coding Theory
Format
Hardcover
Language
English
Series
Graduate Texts in Mathematics Ser.
Publication Year
1998
Type
Textbook
Number of Pages
Xiv, 234 Pages

Dimensions

Item Length
9.3in
Item Height
0.3in
Item Width
6.1in
Item Weight
19.3 Oz

Additional Product Features

Series Volume Number
86
Number of Volumes
1 Vol.
Lc Classification Number
Qa297.4
Edition Description
Expanded,Revised Edition
Edition Number
3
Reviews
From the reviews: "This is a new edition of a well-known and widely used book of van Lint. We can only applaud for the new appearance. [...] I think this textbook will continue to be one of the most favourite textbooks of coding theory." Acta Scient.Math. 67, p.882, 2001   From the reviews: "The 2nd (slightly enlarged) edition of the van Lint's book is a short, concise, mathematically rigorous introduction to the subject. Basic notions and ideas are clearly presented from the mathematician's point of view and illustrated on various special classes of codes...This nice book is a must for every mathematician wishing to introduce himself to the algebraic theory of coding." European Mathematical Society Newsletter, 1993 "Despite the existence of so many other books on coding theory, this present volume will continue to hold its place as one of the standard texts...." The Mathematical Gazette, 1993 J.H. van Lint Introduction to Coding Theory "Despite the existence of so many other books on coding theory, this present volume will continue to hold its place as one of the standard texts."a? THE MATHEMATICAL GAZETTE
Table of Content
1 Mathematical Background.- 1.1. Algebra.- 1.2. Krawtchouk Polynomials.- 1.3. Combinatorial Theory.- 1.4. Probability Theory.- 2 Shannon's Theorem.- 2.1. Introduction.- 2.2. Shannon's Theorem.- 2.3. On Coding Gain.- 2.4. Comments.- 2.5. Problems.- 3 Linear Codes.- 3.1. Block Codes.- 3.2. Linear Codes.- 3.3. Hamming Codes.- 3.4. Majority Logic Decoding.- 3.5. Weight Enumerators.- 3.6. The Lee Metric.- 3.7. Comments.- 3.8. Problems.- 4 Some Good Codes.- 4.1. Hadamard Codes and Generalizations.- 4.2. The Binary Golay Code.- 4.3. The Ternary Golay Code.- 4.4. Constructing Codes from Other Codes.- 4.5. Reed--Muller Codes.- 4.6. Kerdock Codes.- 4.7. Comments.- 4.8. Problems.- 5 Bounds on Codes.- 5.1. Introduction: The Gilbert Bound.- 5.2. Upper Bounds.- 5.3. The Linear Programming Bound.- 5.4. Comments.- 5.5. Problems.- 6 Cyclic Codes.- 6.1. Definitions.- 6.2. Generator Matrix and Check Polynomial.- 6.3. Zeros of a Cyclic Code.- 6.4. The Idempotent of a Cyclic Code.- 6.5. Other Representations of Cyclic Codes.- 6.6. BCH Codes.- 6.7. Decoding BCH Codes.- 6.8. Reed--Solomon Codes.- 6.9. Quadratic Residue Codes.- 6.10. Binary Cyclic Codes of Length 2n(n odd).- 6.11. Generalized Reed--Muller Codes.- 6.12. Comments.- 6.13. Problems.- 7 Perfect Codes and Uniformly Packed Codes.- 7.1. Lloyd's Theorem.- 7.2. The Characteristic Polynomial of a Code.- 7.3. Uniformly Packed Codes.- 7.4. Examples of Uniformly Packed Codes.- 7.5. Nonexistence Theorems.- 7.6. Comments.- 7.7. Problems.- 8 Codes over ?4.- 8.1. Quaternary Codes.- 8.2. Binary Codes Derived from Codes over ?4.- 8.3. Galois Rings over ?4.- 8.4. Cyclic Codes over ?4.- 8.5. Problems.- 9 Goppa Codes.- 9.1. Motivation.- 9.2. Goppa Codes.- 9.3. The Minimum Distance of Goppa Codes.- 9.4. Asymptotic Behaviour of Goppa Codes.- 9.5. Decoding Goppa Codes.- 9.6. Generalized BCH Codes.- 9.7. Comments.- 9.8. Problems.- 10 Algebraic Geometry Codes.- 10.1. Introduction.- 10.2. Algebraic Curves.- 10.3. Divisors.- 10.4. Differentials on a Curve.- 10.5. The Riemann--Roch Theorem.- 10.6. Codes from Algebraic Curves.- 10.7. Some Geometric Codes.- 10.8. Improvement of the Gilbert--Varshamov Bound.- 10.9. Comments.- 10.10.Problems.- 11 Asymptotically Good Algebraic Codes.- 11.1. A Simple Nonconstructive Example.- 11.2. Justesen Codes.- 11.3. Comments.- 11.4. Problems.- 12 Arithmetic Codes.- 12.1. AN Codes.- 12.2. The Arithmetic and Modular Weight.- 12.3. Mandelbaum--Barrows Codes.- 12.4. Comments.- 12.5. Problems.- 13 Convolutional Codes.- 13.1. Introduction.- 13.2. Decoding of Convolutional Codes.- 13.3. An Analog of the Gilbert Bound for Some Convolutional Codes.- 13.4. Construction of Convolutional Codes from Cyclic Block Codes.- 13.5. Automorphisms of Convolutional Codes.- 13.6. Comments.- 13.7. Problems.- Hints and Solutions to Problems.- References.
Copyright Date
1999
Topic
Information Theory, Number Theory, Geometry / Algebraic, Discrete Mathematics
Lccn
98-048080
Intended Audience
Scholarly & Professional
Illustrated
Yes
Genre
Computers, Mathematics

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