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Hedayat A.S., Sloane N.J.A., Stufken J. — Orthogonal Arrays: Theory and Applications
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Название: Orthogonal Arrays: Theory and ApplicationsАвторы: Hedayat A.S., Sloane N.J.A., Stufken J.Аннотация: This is the first book on the subject since its introduction more than fifty years ago, and it can be used as a graduate text or as a reference work. It features all of the key results, many very useful tables, and a large number of research problems. The book will be of interest to those interested in one of the most fascinating areas of discrete mathematics, connected to statistics and coding theory, with applications to computer science and cryptography. It will be useful for anyone who is running experiments, whether in a chemistry lab or a manufacturing plant (trying to make those alloys stronger), or in agricultural or medical research. Sam Hedayat is Professor of Statistics and Senior Scholar in the Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago. Neil J.A. Sloane is with AT&T Bell Labs (now AT&T Labs). John Stufken is Professor Statistics at Iowa State University.
Язык: Рубрика: Математика /Алгебра /Комбинаторика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1999Количество страниц: 416Добавлена в каталог: 11.03.2005Операции: Положить на полку |
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Gilbert — Varshamov bound 229 Godsil and McKay 193 Goethals 102 245 Goethals — Delsarte code 102 Golay 82 99 108 Golay code 99 106 323 Gosset 305 337 339 Graybill 295 Grieg 243 Griesmer 81 Griesmer bound 81 Groops 242 Gross 41 groups 242 Gulati 27 30 Gulati and Kounias 98 108 Gulliver and Bhargava 323 Gulliver and Ostergard 323 hadamard 145 Hadamard array 70 146 148 338 Hadamard conjecture 146 Hadamard determinant problem 163 Hadamard matrices, equivalent 147 Hadamard matrix xi 101 145 338 Hadamard matrix, Paley 152 Hadamard matrix, Sylvester 149 Hadamard matrix, Williamson 153 Hall 141 155 156 159 164 339 Hamada and Wu 307 314 315 Hamming xvi 49 82 108 Hamming bound 78 Hamming code 49 63 91 Hamming distance 62 Hamming weight 61 Hamming — Rao construction 49 Hammons, Kumar, Calderbank, Sloane and Sole 102 228 324 Hanani 222 242 Hardin and Sloane 164 305 337 339 Harwit and Sloane 163 Hashim and Pozdniakov 323 Hedayat 306 Hedayat and Stufken 23 27 195 230 Hedayat and Wallis 162 164 Hedayat, Pn and Stufken 206 330 Hedayat, Raghavarao and Seiden 175 180 Hedayat, Seiden and Stufken 22 34 109 323 Hedayat, Stufken and Su 22 137 323 Helgert and Stinaff 324 Hergert 102 Hexacode 91 Hill 106 109 323 Hill and Newton 323 Hinkelmann and Kempthorne 193 247 265 283 Hirschfeld 98 109 Hirschfeld and Storme 109 Hocquenghem 93 Horn and Johnson 166 Hotelling 163 Hughes and Piper 163 192 Hunter, Hodi and Eager 314 315 Index of orthogonal array 2 Index unity 2 38 Inequivalent Latin squares 193 Information matrix 257 Integral element 343 Interaction effect 252 Irreducible polynomial 347 Isolated Latin square 168 Isomorphic fields 350 Isomorphic Hadamard matrices 147 Isomorphic linear codes 67 Ito, Leon and Longyear 155 164 Itoh and Nakamichi 323 Jacobson 341 Jacobson and Mattheus 194 Jacroux 307 Jacroux and Notz 163 Jacroux, Majumdar and Shah 133 Jaffe 339 john 252 Johnson, Moore and Ylvisaker 84 306 Joshi xvi Jungnickel 115 127 140 141 167 171 173 339 Juxtaposition 4 224 323 Kageyama 17 Kantor 165 Karlin 323 Kempthorne 49 61 66 Kerdock 102 Kerdock code 102 Khuri and Cornell 163 Kiefer 163 Kiefer and Galil 163 Kimura 155 164 Kimura and Ohmori 164 Koehler and Owen 306 Kolesova, Lam and Thiel 193 Korchmaros 109 Kounias and Chadjipantelis 163 Kounias and Farmakis 163 Kounias and Petros 27 Kreher 138 337 Kreher and Radziszowski 138 337 Kreher and Stinson 138 337 Kronecker product 123 Kschischang and Pasupathy 105 106 323 Laihonen 84 Laihonen and Litsyn 84 Lam and Tonchev 109 Lam, Thiel and Swiercz 192 Large set 244 Latin square 168 Latin square, isolated 168 Latin square, normalized 193 Latin square, orthogonally isolated 168 Latin square, random 193 Latin square, reduced 193 Latin square, subsquare of 194 Latin squares, enumeration of 193 Latin squares, equivalent 169 Latin squares, inequivalent 193 Latin squares, mutually orthogonal 168 Latin squares, orthogonal 168 Latin squares, pairwise orthogonal 168 Lattice 335 Laywine and Mullen 167 173 Leon 165 Level combinations 3 248 Levenshtein 78 80 Lexicographic code 323 Lidl and Niederreiter 341 349 354 356 Lin 304 Lin and Stufken 307 Linear code 63 276 Linear F-square 181 Linear orthogonal array 40 54 Linear programming bound xi 32 73 Litsyn 339 Litsyn, Rains and Sloane 339 Lloyd 81 Lloyd polynomial 81 Location effects 298 Mackenzie and Seberry 74 MacNeish 171 MacWilliams 68 MacWilliams and Sloane xiii 27 33 43 69 70 74 76 80 81 83 84 87 223—225 228 229 305 308 323 339 MacWilliams transform 69 MacWilliams, Odlyzko, Sloane and Ward 99 MacWilliams, Sloane and Thompson 192 Main-effect 252 Main-effects 288 Main-effects model 288 Mallows 304 Mallows, Pless and Sloane 99 Mandeli 206 334 Mandeli, Lee and Federer 181 Mandl 305 Manufacturing vii Martin and Stinson 245 Masuyama 127 130 Mathon and Rosa 339 Maurin 195 Maximin distance designs 84 McCarthy x 163 306 McCoy 341 McEliece 83 McEliece et al. bound 229 McEliece, Rodemich, Rumsey and Welch 80 229 McKay and Rogoyski 193 McKay, Beckman and Conover 306 MDS code see code MDS Mead 247 Minimal aberration 306 Minimal distance 62 67 276 Minimal polynomial 93 Mitchell 163 Mixed orthogonal array 6 200 Mixed orthogonal main-effects plan 7 Model 249 Model sum of squares 262 Monic polynomial 345 Monroe and Pless 323 Montgomery 247 250 270 286 307 Mood 163 Morgan and Chakravarti 133 Morris 306 Moyssiadis and Kounias 163 Mukerjee 25 236 237 239 240 306 Mukerjee and Kageyama 17 Mukerjee and Wu 202 Mukhopadhyay 45 130 133 137 Muller 99 Mutually orthogonal Latin squares 168 Myers and Montgomery 247 302 303 Myers, Khuri and Vining 302 Nair xv 299 Nair and Pregibon 302 Namikawa, Fujii and Yamamoto 109 Nearly orthogonal array 338 Net 242 244 Newhart 99 Niederreiter 244 245 Noda 16 17 34 324 Noise factor 299 Nonlinear code 67 69 Nonlinear orthogonal array 67 Nonresidue 358 Nordstrom and Robinson 102 324 Normalized Hadamard matrix 147 Normalized Latin square 193 Numerical integration 244 Order of a Galois field 342 Ordered orthogonal array 244 Orthogonal array over ring 44 Orthogonal array, 2-level 27 Orthogonal array, assemblies of 2 Orthogonal array, binary complement 28 Orthogonal array, complement of 5 Orthogonal array, complementary 5 Orthogonal array, complete 16 Orthogonal array, completely resolvable 119 Orthogonal array, compound 230 Orthogonal array, constraints of 3 Orthogonal array, covering radius 84 Orthogonal array, cyclic 88 Orthogonal array, dimension of 40 Orthogonal array, dual 65 Orthogonal array, fixed-level 199 Orthogonal array, incomplete 195 Orthogonal array, index of 2 Orthogonal array, index unity 2 22 38 79 338 Orthogonal array, level combinations in 3 Orthogonal array, linear 40 54 244 Orthogonal array, maximal factors 11 Orthogonal array, maximin distance 84 Orthogonal array, minimal runs 11 Orthogonal array, mixed xii 184 200 Orthogonal array, nonlinear 67 Orthogonal array, ordered 244 Orthogonal array, parameters of 2 Orthogonal array, perpendicular 133 Orthogonal array, resolvable 119 Orthogonal array, runs of 2 Orthogonal array, saturated 303 Orthogonal array, schematic 245 Orthogonal array, simple 40 Orthogonal array, size of 2 Orthogonal array, strength of 2 Orthogonal array, symbols in 3 Orthogonal array, tight 16 204 303 Orthogonal array, Type I 132 Orthogonal array, Type II 132 Orthogonal array, zero-sum 12 Orthogonal arrays, equivalent 6 Orthogonal arrays, isomorphic 5 34 35 Orthogonal arrays, juxtaposition of 4 34 224 323 Orthogonal arrays, large set of 244 Orthogonal arrays, statistically equivalent 6 34 Orthogonal F-squares 174 Orthogonal Latin squares 168 Orthogonal main-effects plan 7 288 Orthogonal projection matrix 214 Orthogonal treatment contrasts 251 Orthogonally isolated 168 Ovoid 101 Owen x 306 Pairwise orthogonal F-squares xi 174 338 Pairwise orthogonal Latin squares xi 42 168 338 Paley 149 Paley construction 152 Parallel transversals 172 parameter design 299 Parity check matrix 64 65 276 Parker 171 Partially ordered set 335 Pearson xvi Pearson and Hartley 254 Perpendicular array 133 Perpendicular difference array 133 143 Peterson and Weldon 108 Piepel 305 Piret 324 Plackett 289 Plackett and Burman xv 13 146 Plackett — Burman designs 146 Pless 324 Pless and Huffman 83 Plotkin 74 80 Plotkin bound 80 Pointed brackets 90 Polynomial ring 345 Polynomial, irreducible 347 Polynomial, minimal 356 Polynomial, monic 345 Polynomial, primitive 353 Polynomial, reciprocal 89 Preparata 102 Primitive element 46 348 Primitive irreducible polynomial 353 Primitive root 350
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