Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Sphere Packings, Lattices and Groups / / by John Conway, Neil J. A. Sloane
| Sphere Packings, Lattices and Groups / / by John Conway, Neil J. A. Sloane |
| Autore | Conway John |
| Edizione | [3rd ed. 1999.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (LXXIV, 706 p.) |
| Disciplina |
519
511.6 |
| Collana | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| Soggetto topico |
Applied mathematics
Engineering mathematics Group theory Computational intelligence Chemometrics Applications of Mathematics Group Theory and Generalizations Computational Intelligence Math. Applications in Chemistry |
| ISBN | 1-4757-6568-1 |
| Classificazione |
10E30
11T71 20E30 52A45 90Bxx 05B40 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Sphere Packings and Kissing Numbers -- 2 Coverings, Lattices and Quantizers -- 3 Codes, Designs and Groups -- 4 Certain Important Lattices and Their Properties -- 5 Sphere Packing and Error-Correcting Codes -- 6 Laminated Lattices -- 7 Further Connections Between Codes and Lattices -- 8 Algebraic Constructions for Lattices -- 9 Bounds for Codes and Sphere Packings -- 10 Three Lectures on Exceptional Groups -- 11 The Golay Codes and the Mathieu Groups -- 12 A Characterization of the Leech Lattice -- 13 Bounds on Kissing Numbers -- 14 Uniqueness of Certain Spherical Codes -- 15 On the Classification of Integral Quadratic Forms -- 16 Enumeration of Unimodular Lattices -- 17 The 24-Dimensional Odd Unimodular Lattices -- 18 Even Unimodular 24-Dimensional Lattices -- 19 Enumeration of Extremal Self-Dual Lattices -- 20 Finding the Closest Lattice Point -- 21 Voronoi Cells of Lattices and Quantization Errors -- 22 A Bound for the Covering Radius of the Leech Lattice -- 23 The Covering Radius of the Leech Lattice -- 24 Twenty-Three Constructions for the Leech Lattice -- 25 The Cellular Structure of the Leech Lattice -- 26 Lorentzian Forms for the Leech Lattice -- 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice -- 28 Leech Roots and Vinberg Groups -- 29 The Monster Group and its 196884-Dimensional Space -- 30 A Monster Lie Algebra? -- Supplementary Bibliography. |
| Record Nr. | UNINA-9910823188203321 |
Conway John
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The theory of error correcting codes [[electronic resource] /] / F. J. MacWilliams, N. J. A. Sloane
| The theory of error correcting codes [[electronic resource] /] / F. J. MacWilliams, N. J. A. Sloane |
| Autore | MacWilliams F. J (Florence Jessie), <1917-> |
| Pubbl/distr/stampa | Amsterdam ; ; New York, : North-Holland Pub. Co. |
| Descrizione fisica | 1 online resource (787 p.) |
| Disciplina | 516.362 |
| Altri autori (Persone) | SloaneN. J. A <1939-> (Neil James Alexander) |
| Collana | North-Holland mathematical library |
| Soggetto topico |
Error-correcting codes (Information theory)
Coding theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-76978-2
9786612769788 0-08-095423-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; The Theory of Error-Correcting Codes; Copyright Page; Preface; Preface to the third printing; Contents; Chapter 1. Linear codes; 1. Linear codes; 2. Properties of a linear code; 3. At the receiving end; 4. More about decoding a linear code; 5. Error probability; 6. Shannon's theorem on the existence of good codes; 7. Hamming codes; 8. The dual code; 9. Construction of new codes from old (II); 10. Some general properties of a linear code; 11. Summary of Chapter 1; Notes on Chapter 1; Chapter 2. Nonlinear codes, Hadamard matrices, designs and the Golay code; 1. Nonlinear codes
2. The Plotkin bound3. Hadamard matrices and Hadamard codes; 4. Conferences matrices; 5. t-designs; 6. An introduction to the binary Golay code; 7. The Steiner system S(5, 6, 12), and nonlinear single-error correcting codes; 8. An introduction to the Nordstrom-Robinson code; 9. Construction of new codes from old (III); Notes on Chapter 2; Chapter 3. An introduction to BCH codes and finite fields; 1. Double-error-correcting BCH codes (I); 2. Construction of the field GF(16); 3. Double-error-correcting BCH codes (II); 4. Computing in a finite field; Notes on Chapter 3; Chapter 4. Finite fields 1. Introduction2. Finite fields: the basic theory; 3. Minimal polynomials; 4. How to find irreducible polynomials; 5. Tables of small fields; 6. The automorphism group of GF(pm); 7. The number of irreducible polynomials; 8. Bases of GF(pm) over GF(p); 9. Linearized polynomials and normal bases; Notes on Chapter 4; Chapter 5. Dual codes and their weight distribution; 1. Introduction; 2. Weight distribution of the dual of a binary linear code; 3. The group algebra; 4. Characters; 5. MacWilliams theorem for nonlinear codes; 6. Generalized MacWilliams theorems for linear codes 7. Properties of Krawtchouk polynomialsNotes on Chapter 5; Chapter 6. Codes. designs and perfect codes; 1. Introduction; 2. Four fundamental parameters of a code; 3. An explicit formula for the weight and distance distribution; 4. Designs from codes when s = d'; 5. The dual code also gives designs; 6. Weight distribution of translates of a code; 7.Designs from nonlinear codes when s' = d; 8. Perfect codes; 9. Codes over GF(q); 10. There are no more perfect codes; Notes on Chapter 6; Chapter 7. Cyclic codes; 1. Introduction; 2. Definition of a cyclic code; 3. Generator polynomial 4. The check polynomial5. Factors of Xn - 1; 6. t-error-correcting BCH codes; 7. Using a matrix over GF(qn) to define a code over GF(q); 8. Encoding cyclic codes; Notes on Chapter 7; Chapter 8. Cyclic codes (contd.): Idempotents and Mattson-Solomon polynomials; 1. Introduction; 2. Idempotents; 3. Minimal ideals. irreducible codes. and primitive idempotents; 4. Weight distribution of minimal codes; 5. The automorphism group of a code; 6. The Mattson-Solomon polynomial; 7. Some weight distributions; Notes on Chapter 8; Chapter 9. BCH codes; 1. Introduction 2. The true minimum distance of a BCH code |
| Record Nr. | UNINA-9910511895303321 |
|
MacWilliams F. J (Florence Jessie), <1917->
|
||
| Amsterdam ; ; New York, : North-Holland Pub. Co. | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The theory of error correcting codes [[electronic resource] /] / F. J. MacWilliams, N. J. A. Sloane
| The theory of error correcting codes [[electronic resource] /] / F. J. MacWilliams, N. J. A. Sloane |
| Autore | MacWilliams F. J (Florence Jessie), <1917-> |
| Pubbl/distr/stampa | Amsterdam ; ; New York, : North-Holland Pub. Co. |
| Descrizione fisica | 1 online resource (787 p.) |
| Disciplina | 516.362 |
| Altri autori (Persone) | SloaneN. J. A <1939-> (Neil James Alexander) |
| Collana | North-Holland mathematical library |
| Soggetto topico |
Error-correcting codes (Information theory)
Coding theory |
| ISBN |
1-282-76978-2
9786612769788 0-08-095423-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; The Theory of Error-Correcting Codes; Copyright Page; Preface; Preface to the third printing; Contents; Chapter 1. Linear codes; 1. Linear codes; 2. Properties of a linear code; 3. At the receiving end; 4. More about decoding a linear code; 5. Error probability; 6. Shannon's theorem on the existence of good codes; 7. Hamming codes; 8. The dual code; 9. Construction of new codes from old (II); 10. Some general properties of a linear code; 11. Summary of Chapter 1; Notes on Chapter 1; Chapter 2. Nonlinear codes, Hadamard matrices, designs and the Golay code; 1. Nonlinear codes
2. The Plotkin bound3. Hadamard matrices and Hadamard codes; 4. Conferences matrices; 5. t-designs; 6. An introduction to the binary Golay code; 7. The Steiner system S(5, 6, 12), and nonlinear single-error correcting codes; 8. An introduction to the Nordstrom-Robinson code; 9. Construction of new codes from old (III); Notes on Chapter 2; Chapter 3. An introduction to BCH codes and finite fields; 1. Double-error-correcting BCH codes (I); 2. Construction of the field GF(16); 3. Double-error-correcting BCH codes (II); 4. Computing in a finite field; Notes on Chapter 3; Chapter 4. Finite fields 1. Introduction2. Finite fields: the basic theory; 3. Minimal polynomials; 4. How to find irreducible polynomials; 5. Tables of small fields; 6. The automorphism group of GF(pm); 7. The number of irreducible polynomials; 8. Bases of GF(pm) over GF(p); 9. Linearized polynomials and normal bases; Notes on Chapter 4; Chapter 5. Dual codes and their weight distribution; 1. Introduction; 2. Weight distribution of the dual of a binary linear code; 3. The group algebra; 4. Characters; 5. MacWilliams theorem for nonlinear codes; 6. Generalized MacWilliams theorems for linear codes 7. Properties of Krawtchouk polynomialsNotes on Chapter 5; Chapter 6. Codes. designs and perfect codes; 1. Introduction; 2. Four fundamental parameters of a code; 3. An explicit formula for the weight and distance distribution; 4. Designs from codes when s = d'; 5. The dual code also gives designs; 6. Weight distribution of translates of a code; 7.Designs from nonlinear codes when s' = d; 8. Perfect codes; 9. Codes over GF(q); 10. There are no more perfect codes; Notes on Chapter 6; Chapter 7. Cyclic codes; 1. Introduction; 2. Definition of a cyclic code; 3. Generator polynomial 4. The check polynomial5. Factors of Xn - 1; 6. t-error-correcting BCH codes; 7. Using a matrix over GF(qn) to define a code over GF(q); 8. Encoding cyclic codes; Notes on Chapter 7; Chapter 8. Cyclic codes (contd.): Idempotents and Mattson-Solomon polynomials; 1. Introduction; 2. Idempotents; 3. Minimal ideals. irreducible codes. and primitive idempotents; 4. Weight distribution of minimal codes; 5. The automorphism group of a code; 6. The Mattson-Solomon polynomial; 7. Some weight distributions; Notes on Chapter 8; Chapter 9. BCH codes; 1. Introduction 2. The true minimum distance of a BCH code |
| Record Nr. | UNINA-9910781168703321 |
|
MacWilliams F. J (Florence Jessie), <1917->
|
||
| Amsterdam ; ; New York, : North-Holland Pub. Co. | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The theory of error correcting codes / / F. J. MacWilliams, N. J. A. Sloane
| The theory of error correcting codes / / F. J. MacWilliams, N. J. A. Sloane |
| Autore | MacWilliams F. J (Florence Jessie), <1917-> |
| Pubbl/distr/stampa | Amsterdam ; ; New York, : North-Holland Pub. Co. |
| Descrizione fisica | 1 online resource (787 p.) |
| Disciplina | 516.362 |
| Altri autori (Persone) | SloaneN. J. A <1939-> (Neil James Alexander) |
| Collana | North-Holland mathematical library |
| Soggetto topico |
Error-correcting codes (Information theory)
Coding theory |
| ISBN |
1-282-76978-2
9786612769788 0-08-095423-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; The Theory of Error-Correcting Codes; Copyright Page; Preface; Preface to the third printing; Contents; Chapter 1. Linear codes; 1. Linear codes; 2. Properties of a linear code; 3. At the receiving end; 4. More about decoding a linear code; 5. Error probability; 6. Shannon's theorem on the existence of good codes; 7. Hamming codes; 8. The dual code; 9. Construction of new codes from old (II); 10. Some general properties of a linear code; 11. Summary of Chapter 1; Notes on Chapter 1; Chapter 2. Nonlinear codes, Hadamard matrices, designs and the Golay code; 1. Nonlinear codes
2. The Plotkin bound3. Hadamard matrices and Hadamard codes; 4. Conferences matrices; 5. t-designs; 6. An introduction to the binary Golay code; 7. The Steiner system S(5, 6, 12), and nonlinear single-error correcting codes; 8. An introduction to the Nordstrom-Robinson code; 9. Construction of new codes from old (III); Notes on Chapter 2; Chapter 3. An introduction to BCH codes and finite fields; 1. Double-error-correcting BCH codes (I); 2. Construction of the field GF(16); 3. Double-error-correcting BCH codes (II); 4. Computing in a finite field; Notes on Chapter 3; Chapter 4. Finite fields 1. Introduction2. Finite fields: the basic theory; 3. Minimal polynomials; 4. How to find irreducible polynomials; 5. Tables of small fields; 6. The automorphism group of GF(pm); 7. The number of irreducible polynomials; 8. Bases of GF(pm) over GF(p); 9. Linearized polynomials and normal bases; Notes on Chapter 4; Chapter 5. Dual codes and their weight distribution; 1. Introduction; 2. Weight distribution of the dual of a binary linear code; 3. The group algebra; 4. Characters; 5. MacWilliams theorem for nonlinear codes; 6. Generalized MacWilliams theorems for linear codes 7. Properties of Krawtchouk polynomialsNotes on Chapter 5; Chapter 6. Codes. designs and perfect codes; 1. Introduction; 2. Four fundamental parameters of a code; 3. An explicit formula for the weight and distance distribution; 4. Designs from codes when s = d'; 5. The dual code also gives designs; 6. Weight distribution of translates of a code; 7.Designs from nonlinear codes when s' = d; 8. Perfect codes; 9. Codes over GF(q); 10. There are no more perfect codes; Notes on Chapter 6; Chapter 7. Cyclic codes; 1. Introduction; 2. Definition of a cyclic code; 3. Generator polynomial 4. The check polynomial5. Factors of Xn - 1; 6. t-error-correcting BCH codes; 7. Using a matrix over GF(qn) to define a code over GF(q); 8. Encoding cyclic codes; Notes on Chapter 7; Chapter 8. Cyclic codes (contd.): Idempotents and Mattson-Solomon polynomials; 1. Introduction; 2. Idempotents; 3. Minimal ideals. irreducible codes. and primitive idempotents; 4. Weight distribution of minimal codes; 5. The automorphism group of a code; 6. The Mattson-Solomon polynomial; 7. Some weight distributions; Notes on Chapter 8; Chapter 9. BCH codes; 1. Introduction 2. The true minimum distance of a BCH code |
| Record Nr. | UNINA-9910818005503321 |
|
MacWilliams F. J (Florence Jessie), <1917->
|
||
| Amsterdam ; ; New York, : North-Holland Pub. Co. | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||