Introduction to the theory of error-correcting codes / / Vera Pless

• Autore: Pless Vera
• Pubblicazione: New York, New York : , : John Wiley & Sons, Inc., , 1998; ©1998
• Edizione: 3rd ed.
• Descrizione fisica: 1 online resource (226 p.)
• Disciplina: 003.54; 005.7/2; 005.72
• Soggetto topico: Error-correcting codes (Information theory)
• Soggetto genere / forma: Electronic books.
• Note generali: "A Wiley-Interscience Publication."
• Nota di bibliografia: Includes bibliographical references and index.
• 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
• Sommario/riassunto: A complete introduction to the many mathematical tools used to solve practical problems in coding.Mathematicians have been fascinated with the theory of error-correcting codes since the publication of Shannon's classic papers fifty years ago. With the proliferation of communications systems, computers, and digital audio devices that employ error-correcting codes, the theory has taken on practical importance in the solution of coding problems. This solution process requires the use of a wide variety of mathematical tools and an understanding of how to find mathematical techniques to sol
• Titolo autorizzato: Introduction to the theory of error-correcting codes
• ISBN: 1-283-33200-0; 9786613332004; 1-118-03274-8; 1-118-03099-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910141176103321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley-Interscience series in discrete mathematics and optimization.