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Introduction to Coding Theory /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint : Springer,
1992.
|
| Edición: | Second edition. |
| Colección: | Graduate texts in mathematics ;
86. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Lint, J. H. | |
| 245 | 1 | 0 | |a Introduction to Coding Theory / |c by J.H. Lint. |
| 250 | |a Second edition. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint : |b Springer, |c 1992. | ||
| 300 | |a 1 online resource (XII, 186 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Graduate Texts in Mathematics, 0072-5285 ; |v 86 | |
| 520 | |a 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 chapter is a memory-refresher reviewing the prerequisite mathematical knowledge. The body of the book contains two parts (five chapters each): a rigorous mathematically oriented first course in coding theory, followedby introductions to special topics; these can be used as a second semester, as supplementary reading, or as preparation for studying the literature. Among the special features are chapters on arithmetic codes and convolutional codes, and exercises with complete solutions. | ||
| 505 | 0 | |a 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. | |
| 504 | |a Includes bibliographical references and index. | ||
| 546 | |a English. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Mathematics. | |
| 650 | 0 | |a Combinatorial analysis. | |
| 650 | 0 | |a Number theory. | |
| 650 | 6 | |a Mathématiques. | |
| 650 | 6 | |a Analyse combinatoire. | |
| 650 | 6 | |a Théorie des nombres. | |
| 650 | 7 | |a mathematics. |2 aat | |
| 650 | 7 | |a applied mathematics. |2 aat | |
| 650 | 7 | |a Combinatorial analysis |2 fast | |
| 650 | 7 | |a Mathematics |2 fast | |
| 650 | 7 | |a Number theory |2 fast | |
| 776 | 0 | 8 | |i Printed edition: |z 9783662001769 |
| 830 | 0 | |a Graduate texts in mathematics ; |v 86. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3098533 |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL3098533 | ||
| 938 | |a YBP Library Services |b YANK |n 13364534 | ||
| 994 | |a 92 |b IZTAP | ||