Cargando…

Introduction to Coding Theory /

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 relati...

Descripción completa

Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Lint, J. H.
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint : Springer, 1999.
Edición:	Third rev. and Expanded edition.
Colección:	Graduate texts in mathematics ; 86.
Temas:	Coding theory. Coding theory
Acceso en línea:	Texto completo

Tabla de Contenidos:

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.

Introduction to Coding Theory /

Ejemplares similares