Introduction to coding theory. Graduate texts in mathematics 86 - copertina rigida, flessible

EAN (ISBN-13): 9783540548942
ISBN (ISBN-10): 3540548947
Copertina rigida
Anno di pubblicazione: 1992
Editore: Springer

Libro nella banca dati dal 2007-06-26T09:41:37+02:00 (Zurich)
Pagina di dettaglio ultima modifica in 2024-03-23T23:23:23+01:00 (Zurich)
ISBN/EAN: 3540548947

ISBN - Stili di scrittura alternativi:
3-540-54894-7, 978-3-540-54894-2
Stili di scrittura alternativi e concetti di ricerca simili:
Autore del libro : van lint
Titolo del libro: mathematics berlin, introduction coding theory, graduate text mathematics, graduate texts mathematics

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Dati dell'editore

Autore: J.H. van Lint
Titolo: Graduate Texts in Mathematics; Introduction to Coding Theory
Editore: Springer; Springer Berlin
186 Pagine
Anno di pubblicazione: 1992-07-02
Berlin; Heidelberg; DE
Stampato / Fatto in
Peso: 0,435 kg
Lingua: Inglese
85,59 € (DE)
87,99 € (AT)
106,60 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Zahlentheorie; Verstehen; coding theory; discrete mathematics; code; coding; C; Number Theory; Mathematics and Statistics; Combinatorics; Kombinatorik und Graphentheorie; BB; BB; BC; EA

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.
Revised and expanded edition. Well-suited as textbook for lectures. The text contains numerous problems with solutions, as well as a lot of examples.