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Introduction to the theory of error-correcting codes / / Vera Pless
| Introduction to the theory of error-correcting codes / / Vera Pless |
| Autore | Pless Vera |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 1998 |
| Descrizione fisica | 1 online resource (226 p.) |
| Disciplina |
003.54
005.7/2 005.72 |
| Collana | Wiley-Interscience Series in Discrete Mathematics and Optimization |
| Soggetto topico | Error-correcting codes (Information theory) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-33200-0
9786613332004 1-118-03274-8 1-118-03099-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Introduction to the Theory of Error-Correcting Codes; Contents; Preface; 1 Introductory Concepts; 1.1 Introduction; 1.2 Basic Definitions; 1.3 Weight, Minimum Weight, and Maximum-Likelihood Decoding; Problems; 2 Useful Background; 2.1 Syndrome Decoding; 2.2 Perfect Codes, Hamming Codes, Sphere-Packing Bound; 2.3 Packing Radius, Covering Radius, MDS Codes, and Some Bounds; 2.4 Self-Dual Codes, Golay Codes; 2.5 Reed-Muller Codes; 2.6 Puncturing, Extending, and Shortening; Problems; 3 A Double-Error-Correcting BCH Code and a Finite Field of 16 Elements; 3.1 The Problem; 3.2 Polynomials
3.3 A Finite Field of 16 Elements3.4 Double-Error-Correcting Bose-Chaudhuri-Hocquenghem (BCH) Code; Problems; 4 Finite Fields; 4.1 Groups; 4.2 Structure of a Finite Field; 4.3 Minimal Polynomials; 4.4 Factoring xn - 1; Problems; 5 Cyclic Codes; 5.1 Origin and Definition of Cyclic Codes; 5.2 How to Find Cyclic Codes: The Generator Polynomial; 5.3 Generator Polynomial of the Dual Code; 5.4 Idempotents and Minimal Ideals for Binary Cyclic Codes; Problems; 6 Group of a Code and Quadratic Residue (QR) Codes; 6.1 Some Cyclic Codes We Know; 6.2 Permutation Groups; 6.3 Group of a Code 6.4 Definition of Quadratic Residue (QR) Codes6.5 Extended QR Codes, Square Root Bound, and Groups of QR Codes; 6.6 Permutation Decoding; 6.7 Decoding the Golay Code; Problems; 7 Bose-Chaudhuri-Hocquenghem (BCH) Codes; 7.1 Cyclic Codes Given in Terms of Roots; 7.2 Vandermonde Determinants; 7.3 Definition and Properties of BCH Codes; 7.4 Reed-Solomon Codes; 7.5 More on the Minimum Distance; 7.6 Decoding BCH Codes; Problems; 8 Weight Distributions; 8.1 Preliminary Concepts and a Theorem on Weights in Homogeneous Codes; 8.2 MacWilliams Equations; 8.3 Pless Power Moments; 8.4 Gleason Polynomials Problems9 Designs and Games; 9.1 Designs; 9.2 Designs and Codes; 9.3 Assmus-Mattson Theorem and a Design-Decoding Scheme; 9.4 Symmetry Codes; 9.5 Games; 9.6 Games and Codes; 9.7 Greedy Codes; Problems; 10 Some Codes Are Unique; 10.1 The Hamming Code and the Ternary Golay Code Are Unique; 10.2 The Steiner System S(5, 8, 24) Is Unique and So Is a Binary [24, 12, 8] Code; 10.3 ""Glue""; 10.4 Residual Codes and the Griesmer Bound; 10.5 Some Nonlinear Codes; 10.6 Z4 Codes and Their Gray Images; Problems; Appendix; References; Index |
| Record Nr. | UNINA-9910141176103321 |
Pless Vera
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to the theory of error-correcting codes / / Vera Pless
| Introduction to the theory of error-correcting codes / / Vera Pless |
| Autore | Pless Vera |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 1998 |
| Descrizione fisica | 1 online resource (226 p.) |
| Disciplina |
003.54
005.7/2 005.72 |
| Collana | Wiley-Interscience Series in Discrete Mathematics and Optimization |
| Soggetto topico | Error-correcting codes (Information theory) |
| ISBN |
1-283-33200-0
9786613332004 1-118-03274-8 1-118-03099-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Introduction to the Theory of Error-Correcting Codes; Contents; Preface; 1 Introductory Concepts; 1.1 Introduction; 1.2 Basic Definitions; 1.3 Weight, Minimum Weight, and Maximum-Likelihood Decoding; Problems; 2 Useful Background; 2.1 Syndrome Decoding; 2.2 Perfect Codes, Hamming Codes, Sphere-Packing Bound; 2.3 Packing Radius, Covering Radius, MDS Codes, and Some Bounds; 2.4 Self-Dual Codes, Golay Codes; 2.5 Reed-Muller Codes; 2.6 Puncturing, Extending, and Shortening; Problems; 3 A Double-Error-Correcting BCH Code and a Finite Field of 16 Elements; 3.1 The Problem; 3.2 Polynomials
3.3 A Finite Field of 16 Elements3.4 Double-Error-Correcting Bose-Chaudhuri-Hocquenghem (BCH) Code; Problems; 4 Finite Fields; 4.1 Groups; 4.2 Structure of a Finite Field; 4.3 Minimal Polynomials; 4.4 Factoring xn - 1; Problems; 5 Cyclic Codes; 5.1 Origin and Definition of Cyclic Codes; 5.2 How to Find Cyclic Codes: The Generator Polynomial; 5.3 Generator Polynomial of the Dual Code; 5.4 Idempotents and Minimal Ideals for Binary Cyclic Codes; Problems; 6 Group of a Code and Quadratic Residue (QR) Codes; 6.1 Some Cyclic Codes We Know; 6.2 Permutation Groups; 6.3 Group of a Code 6.4 Definition of Quadratic Residue (QR) Codes6.5 Extended QR Codes, Square Root Bound, and Groups of QR Codes; 6.6 Permutation Decoding; 6.7 Decoding the Golay Code; Problems; 7 Bose-Chaudhuri-Hocquenghem (BCH) Codes; 7.1 Cyclic Codes Given in Terms of Roots; 7.2 Vandermonde Determinants; 7.3 Definition and Properties of BCH Codes; 7.4 Reed-Solomon Codes; 7.5 More on the Minimum Distance; 7.6 Decoding BCH Codes; Problems; 8 Weight Distributions; 8.1 Preliminary Concepts and a Theorem on Weights in Homogeneous Codes; 8.2 MacWilliams Equations; 8.3 Pless Power Moments; 8.4 Gleason Polynomials Problems9 Designs and Games; 9.1 Designs; 9.2 Designs and Codes; 9.3 Assmus-Mattson Theorem and a Design-Decoding Scheme; 9.4 Symmetry Codes; 9.5 Games; 9.6 Games and Codes; 9.7 Greedy Codes; Problems; 10 Some Codes Are Unique; 10.1 The Hamming Code and the Ternary Golay Code Are Unique; 10.2 The Steiner System S(5, 8, 24) Is Unique and So Is a Binary [24, 12, 8] Code; 10.3 ""Glue""; 10.4 Residual Codes and the Griesmer Bound; 10.5 Some Nonlinear Codes; 10.6 Z4 Codes and Their Gray Images; Problems; Appendix; References; Index |
| Record Nr. | UNINA-9910829966703321 |
|
Pless Vera
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||