The theory of error correcting codes / / F. J. MacWilliams, N. J. A. Sloane

• Autore: MacWilliams F. J (Florence Jessie), <1917->
• Pubblicazione: Amsterdam ; ; New York, : North-Holland Pub. Co.; New York, : sole distributors for the U.S.A. and Canada, Elsevier/North-Holland, 1977
• Descrizione fisica: 1 online resource (787 p.)
• Disciplina: 516.362
• Soggetto topico: Error-correcting codes (Information theory); Coding theory
• Altri autori: SloaneN. J. A <1939-> (Neil James Alexander)
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• 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
• Sommario/riassunto: This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.
• Titolo autorizzato: The theory of error correcting codes
• ISBN: 1-282-76978-2; 9786612769788; 0-08-095423-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910818005503321
• Lo trovi qui: Univ. Federico II
• Serie: North-Holland mathematical library ; ; v. 16.