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[null,"1.","Record Nr.",null,"UNINA9910141176103321"]
[null,null,"Autore",null,"Pless Vera"]
[null,null,"Titolo",null,"Introduction to the theory of error-correcting codes / / Vera Pless"]
[null,null,"Pubbl/distr/stampa",null,"New York, New York : , : John Wiley & Sons, Inc., , 1998"]
[{"$nulls":4},"©1998"]
[null,null,"ISBN",null,"1-283-33200-0"]
[{"$nulls":4},"9786613332004"]
[{"$nulls":4},"1-118-03274-8"]
[{"$nulls":4},"1-118-03099-0"]
[null,null,"Edizione",null,"[3rd ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (226 p.)"]
[null,null,"Collana",null,"Wiley-Interscience Series in Discrete Mathematics and Optimization"]
[null,null,"Disciplina",null,"003.54"]
[{"$nulls":4},"005.7/2"]
[{"$nulls":4},"005.72"]
[null,null,"Soggetti",null,"Error-correcting codes (Information theory)"]
[{"$nulls":4},"Electronic books."]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","\"A Wiley-Interscience Publication.\""]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Introduction to the Theory of Error-Correcting Codes; Contents; Preface; 1 Introductory Concepts; 1.1 Introduction; 1.2 Basic Definitions; 1.3 Weight, Minimum Weight, and Maximum-Likelihood Decoding; Problems; 2 Useful Background; 2.1 Syndrome Decoding; 2.2 Perfect Codes, Hamming Codes, Sphere-Packing Bound; 2.3 Packing Radius, Covering Radius, MDS Codes, and Some Bounds; 2.4 Self-Dual Codes, Golay Codes; 2.5 Reed-Muller Codes; 2.6 Puncturing, Extending, and Shortening; Problems; 3 A Double-Error-Correcting BCH Code and a Finite Field of 16 Elements; 3.1 The Problem; 3.2 Polynomials"]
[{"$nulls":4},"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"]
[{"$nulls":4},"6.4 Definition of Quadratic Residue (QR) Codes6.5 Extended QR Codes, Square Root Bound, and Groups of QR Codes; 6.6 Permutation Decoding; 6.7 Decoding the Golay Code; Problems; 7 Bose-Chaudhuri-Hocquenghem (BCH) Codes; 7.1 Cyclic Codes Given in Terms of Roots; 7.2 Vandermonde Determinants; 7.3 Definition and Properties of BCH Codes; 7.4 Reed-Solomon Codes; 7.5 More on the Minimum Distance; 7.6 Decoding BCH Codes; Problems; 8 Weight Distributions; 8.1 Preliminary Concepts and a Theorem on Weights in Homogeneous Codes; 8.2 MacWilliams Equations; 8.3 Pless Power Moments; 8.4 Gleason Polynomials"]
[{"$nulls":4},"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"]
[null,null,null,"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"]