LEADER 04715nam 2200625 450 001 9910829966703321 005 20230421053823.0 010 $a1-283-33200-0 010 $a9786613332004 010 $a1-118-03274-8 010 $a1-118-03099-0 035 $a(CKB)2670000000133886 035 $a(EBL)694736 035 $a(OCoLC)768243484 035 $a(SSID)ssj0000554958 035 $a(PQKBManifestationID)11939877 035 $a(PQKBTitleCode)TC0000554958 035 $a(PQKBWorkID)10517434 035 $a(PQKB)11294617 035 $a(MiAaPQ)EBC694736 035 $a(EXLCZ)992670000000133886 100 $a20160816h19981998 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to the theory of error-correcting codes /$fVera Pless 205 $a3rd ed. 210 1$aNew York, New York :$cJohn Wiley & Sons, Inc.,$d1998. 210 4$dİ1998 215 $a1 online resource (226 p.) 225 1 $aWiley-Interscience Series in Discrete Mathematics and Optimization 300 $a"A Wiley-Interscience Publication." 311 $a0-471-19047-0 320 $aIncludes bibliographical references and index. 327 $aIntroduction 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 327 $a3.3 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 327 $a6.4 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 327 $aProblems9 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 330 $aA complete introduction to the many mathematical tools used to solve practical problems in coding.Mathematicians have been fascinated with the theory of error-correcting codes since the publication of Shannon's classic papers fifty years ago. With the proliferation of communications systems, computers, and digital audio devices that employ error-correcting codes, the theory has taken on practical importance in the solution of coding problems. This solution process requires the use of a wide variety of mathematical tools and an understanding of how to find mathematical techniques to sol 410 0$aWiley-Interscience series in discrete mathematics and optimization. 606 $aError-correcting codes (Information theory) 615 0$aError-correcting codes (Information theory) 676 $a003.54 676 $a005.7/2 676 $a005.72 700 $aPless$b Vera$0440766 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910829966703321 996 $aIntroduction to the theory of error-correcting codes$978888 997 $aUNINA