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Introduction to Coding Theory [[electronic resource] /] / by J.H. van Lint
Introduction to Coding Theory [[electronic resource] /] / by J.H. van Lint
Autore Lint J.H. van
Edizione [3rd ed. 1999.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1999
Descrizione fisica 1 online resource (XIV, 234 p.)
Disciplina 003/.54
Collana Graduate Texts in Mathematics
Soggetto topico Combinatorics
Algebraic geometry
Number theory
Algebraic Geometry
Number Theory
ISBN 3-540-64133-5
3-642-58575-2
Classificazione 94A24
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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.
Record Nr. UNINA-9910478911903321
Lint J.H. van  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1999
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Introduction to Coding Theory [[electronic resource] /] / by J.H. van Lint
Introduction to Coding Theory [[electronic resource] /] / by J.H. van Lint
Autore Lint J.H. van
Edizione [3rd ed. 1999.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1999
Descrizione fisica 1 online resource (XIV, 234 p.)
Disciplina 003/.54
Collana Graduate Texts in Mathematics
Soggetto topico Combinatorics
Algebraic geometry
Number theory
Algebraic Geometry
Number Theory
ISBN 3-540-64133-5
3-642-58575-2
Classificazione 94A24
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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.
Record Nr. UNINA-9910789214503321
Lint J.H. van  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1999
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Introduction to Coding Theory / / by J.H. van Lint
Introduction to Coding Theory / / by J.H. van Lint
Autore Lint Jacobus Hendricus van <1932->
Edizione [3rd ed. 1999.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1999
Descrizione fisica 1 online resource (XIV, 234 p.)
Disciplina 003/.54
Collana Graduate Texts in Mathematics
Soggetto topico Discrete mathematics
Geometry, Algebraic
Number theory
Discrete Mathematics
Algebraic Geometry
Number Theory
ISBN 3-540-64133-5
3-642-58575-2
Classificazione 94A24
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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.
Record Nr. UNINA-9910967034203321
Lint Jacobus Hendricus van <1932->  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1999
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Introduction to Coding Theory [[electronic resource] /] / by J.H. van Lint
Introduction to Coding Theory [[electronic resource] /] / by J.H. van Lint
Autore Lint J.H. van
Edizione [2nd ed. 1992.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1992
Descrizione fisica 1 online resource (XII, 186 p. 11 illus.)
Disciplina 512.7
Collana Graduate Texts in Mathematics
Soggetto topico Number theory
Combinatorics
Number Theory
ISBN 3-662-00174-8
Classificazione 94A24
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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.
Record Nr. UNINA-9910479947203321
Lint J.H. van  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1992
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Introduction to Coding Theory [[electronic resource] /] / by J.H. van Lint
Introduction to Coding Theory [[electronic resource] /] / by J.H. van Lint
Autore Lint J.H. van
Edizione [2nd ed. 1992.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1992
Descrizione fisica 1 online resource (XII, 186 p. 11 illus.)
Disciplina 512.7
Collana Graduate Texts in Mathematics
Soggetto topico Number theory
Combinatorics
Number Theory
ISBN 3-662-00174-8
Classificazione 94A24
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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.
Record Nr. UNINA-9910789216903321
Lint J.H. van  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1992
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Introduction to Coding Theory / / by J.H. van Lint
Introduction to Coding Theory / / by J.H. van Lint
Autore Lint Jacobus Hendricus van <1932->
Edizione [2nd ed. 1992.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1992
Descrizione fisica 1 online resource (XII, 186 p. 11 illus.)
Disciplina 512.7
Collana Graduate Texts in Mathematics
Soggetto topico Number theory
Discrete mathematics
Number Theory
Discrete Mathematics
ISBN 3-662-00174-8
Classificazione 94A24
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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.
Record Nr. UNINA-9910967036903321
Lint Jacobus Hendricus van <1932->  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1992
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui