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Introduction to Coding Theory / by J.H. Lint.

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The first edition of this book was very well received and is considered to be one of the classical introductions to the subject of discrete mathematics- a field that is still growing in importance as the need for mathematiciansand computer scientists in industry continues to grow. The opening chapte...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Lint, J. H.
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint : Springer, 1992.
Edition:Second edition.
Series:Graduate texts in mathematics ; 86.
Subjects:
Mathematics.
Combinatorial analysis.
Number theory.
Table of Contents:
  • 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. Comments
  • 2.4. 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. Comments
  • 3.7. 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 and Algebraic Geometry Codes
  • 6.9. Quadratic Residue Codes
  • 6.10. Binary Cyclic codes of length 2n (n odd)
  • 6.11. Comments
  • 6.12. 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 Goppa Codes
  • 8.1. Motivation
  • 8.2. Goppa Codes
  • 8.3. The Minimum Distance of Goppa Codes
  • 8.4. Asymptotic Behaviour of Goppa Codes
  • 8.5. Decoding Goppa Codes
  • 8.6. Generalized BCH Codes
  • 8.7. Comments
  • 8.8. Problems
  • 9 Asymptotically Good Algebraic Codes
  • 9.1. A Simple Nonconstructive Example
  • 9.2. Justesen Codes
  • 9.3. Comments
  • 9.4. Problems
  • 10 Arithmetic Codes
  • 10.1. AN Codes
  • 10.2. The Arithmetic and Modular Weight
  • 10.3. Mandelbaum-Barrows Codes
  • 10.4. Comments
  • 10.5. Problems
  • 11 Convolutional Codes
  • 11.1. Introduction
  • 11.2. Decoding of Convolutional Codes
  • 11.3. An Analog of the Gilbert Bound for Some Convolutional Codes
  • 11.4. Construction of Convolutional Codes from Cyclic Block Codes
  • 11.5. Automorphisms of Convolutional Codes
  • 11.6. Comments
  • 11.7. Problems
  • Hints and Solutions to Problems
  • References.

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