Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Ericson T. — Codes on Euclidean Spheres
Ericson T. — Codes on Euclidean Spheres

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Codes on Euclidean Spheres

Автор: Ericson T.

Аннотация:

Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. Mathematically the topic belongs to the realm of algebraic combinatorics, with close connections to number theory, geometry, combinatorial theory, and - of course - to algebraic coding theory. The connections to physics occur within areas like crystallography and nuclear physics. In engineering spherical codes are of central importance in connection with error-control in communication systems. In that context the use of spherical codes is often referred to as "coded modulation."


The book offers a first complete treatment of the mathematical theory of codes on Euclidean spheres. Many new results are published here for the first time. Engineering applications are emphasized throughout the text. The theory is illustrated by many examples. The book also contains an extensive table of best known spherical codes in dimensions 3-24, including exact constructions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 564

Добавлена в каталог: 04.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
1-Factor      296
600-cell      10
action      205
Addition formula      33
Algebra      263
Algebra, Bose — Mesner      263
Algorithm, Chase      403
Algorithm, GMD      392 398
Algorithm, soft decision      399
Alphabet      117 130 138 211
Alphabet, hexagonal      197
Alphabet, mixed      213
Alphabet, non-symmetric      220
Alphabet, normalized      220
Antiprism, square      73 80 254
Array intersection      279
Association scheme      11 258
Association scheme, class      258
Association scheme, metric      276
Basis      4
Basis, lattice, $D_n$      355
Biangle, spherical      444
Border      243
Borderline      82
Bound, absolute      292 311
Bound, Bassalygo — Elias      351
Bound, BCH      433
Bound, Boyvalenkov — Danev — Bumova      86
Bound, Chabauty — Shannon — Wyner      19 21
Bound, Coxeter — Boeroeczky      97
Bound, Fejes Toth      82 86 350 443
Bound, first Rankin      40
Bound, Gilbert — Varshamov      19
Bound, Johnson      180 427 429
Bound, Kabatianskii — Levenshtein      23 350 351 353
Bound, Levenshtein      23 47 50 56 60 62 86 157 180
Bound, Lindsey      352
Bound, linear programming      39 62
Bound, Minkowski      352
Bound, Plotkin      17 420
Bound, product      155
Bound, Rankin      14—16 86 180
Bound, Rogers'      350
Bound, Singleton      431
Bound, sphere packing      20 421
Bound, third Rankin      40
Cap, spherical      19 440
Code energy      6 11
Code extension      170
Code group      206 212 213 215 423
Code group, abelian      224
Code group, constant weight      216
Code group, dual      225
Code group, nonplanar      209
Code length      417
Code matrices, equivalent      4
Code, alphabet      5
Code, antipodal      313
Code, BCH      426 433
Code, Best      423
Code, binary      214
Code, binary unrestricted      417
Code, binary, antipodal      255
Code, binary, Biorthogonal      159 419
Code, biorthogonal      18 70 80 107 119 157 158 163 202 220 255 314 324 325 328
Code, concatenation      129 141
Code, conference matrix      160 421
Code, constant energy      11 390
Code, constant weight      179 220
Code, dimension      1 417
Code, distance      417
Code, distance regular      258 318
Code, dominating      112 119 208
Code, dual      225
Code, equivalent      4
Code, Goethals      199
Code, Golay      167 365 381 424
Code, Golay, binary      365 503
Code, Golay, ternary      197 431
Code, Golay, Turyn construction      424
Code, Hadamard      375 419
Code, Hamming      421 430 431
Code, Hamming, binary      372 374
Code, Hamming, binary extended      220
Code, Hamming, ternary      357 372 377
Code, Hexacode      378 433
Code, incompatible      208
Code, inner      129
Code, irreducible      88
Code, Kerdock      157 199 424
Code, linear      214 417
Code, maximal      21
Code, MDS      431
Code, minimum distance      1
Code, nonplanar      208
Code, Nordstrom — Robinson      157 423 425
Code, optimal      14 68 248
Code, optimal, irreducible      91
Code, outer      129
Code, perfect      421
Code, permutation      107 206 213
Code, planar      5
Code, polyphase      195 200 212 255 263
Code, Preparata      199 424
Code, reducible      88
Code, Reed — Muller      365 381 423
Code, Reed — Solomon      426 432
Code, regular      196 210 317 318
Code, Simplex      7 18 107 115 157 201 255 271 312 325 328 330 350
Code, size      1 417
Code, spherical      1 213
Code, spherical, biorthogonal      64 452
Code, spherical, regular      261
Code, spherical, simplex      64
Code, spherical, upper bound      39
Code, subfield subcode      433
Code, tetra      431
Code, trellis      200
Codeword      1
Coefficients, Gegenbauer      37
Complexity, algebraic      391
Complexity, algorithmic      2
composition      371
Concatenation      10
Concatenation, binary balanced      189
Concatenation, generalized      200 201
Condition, crystallographic      345
Condition, integrality      289
Condition, Schlaefli      330
Conditions separation      50
Cone, convex      242
Construction, $Y_3$      222
Construction, $Y_4$      222
Construction, $\mathbb{P}_A(C)$      363
Construction, A      362
Construction, B      363
Construction, Paley      159
Correlation, binary      162 181 427
Correlation, Euclidean      181
Cosine Theorem      446
Criterion, Boyvalenkov — Danev — Bumova      58 62
Cube, snub      78 80 151 254
Cubeoctahedron      115 261 271
CYCLE      89 100
Cycle of length m      89
Cycle, length of      101
Decoder, Chase      400
Decoding, algebraic      391
Decoding, bounded minimum distance      403
Decoding, complexity      390
Decoding, GMD      395
Decoding, maximum likelihood      124
Decoding, parallel      404
Decoding, soft      389
Decoding, successive      410
Degree      311
Degree of face      89
Degree of vertex      88
Degree, monomial      28
Degree, spherical polynomial      28
density      349
Density of lattice      340
Density, center      340 349
Density, packing      340
Design, quasi-symmetric      300 301
Design, spherical      64 314 316
Design, spherical, tight      64 324
Design, strength of      314
Design, symmetric      301
Distance      224
Distance between codes      162
Distance distribution      209 228
Distance distribution of code      228
Distance distribution of dual code      228
Distance distribution, abelian group code      226
Distance, angular      88
Distance, Euclidean      6 88
Distance, graph      275
Distance, Hamming      417
Distance, minimum, angular      88
Distance, minimum, of lattice      339
distribution      108
Distribution weight, complete      372 377
Distribution weight, Hamming      372
dodecahedron      80 325 334
Domain, fundamental      242 244
Duality      298
Duality between codes      223
Edges, parallel      101
Eigenspace      265
Eigenvalue      265
Eigenvalue, dual      268
Eigenvalue, multiplicity      289
Enumeration function, weight, complete      372
Equivalence, geometric      235
Excess of spherical triangle      445
Excess Theorem      444
Expansion, Gegenbauer      38 39 51 61
Expansion, monomial      28
Extension, Coxeter — Boeroeczky      97 350
Extension, trivial      452
Face      89 100
Factor      296
Factorization      296
Formula, addition      32
Formula, Euler's      84 449
Formula, Gauss — Jacobi      46 53 60
Formula, Gauss — Jacobi, modified      59
Function, characteristic      227
Function, indicator      226
Function, indicator, dual code      226
Function, Levenshtein      56 57
Function, positive definite      37
Function, positive definite, product      38
Function, Riemann zeta      353
Function, Schlaefi      98
Function, test      39 51 52 60
Function, test, extreme      56
Function, theta      367
Gegenbauer polynomial orthogonality condition      34
Geometry, spherical      82 443
Golden section      76
Gram matrix      317
Graph, 2-connected      101
Graph, Clebsch      287 294
Graph, cocktail party      290
Graph, conferene      288
Graph, connected      238 286
Graph, Coxeter      236 248
Graph, Coxeter, connected      238
Graph, Coxeter, equivalent      237
Graph, Coxeter, weighted      237
Graph, cube      72
Graph, diameter      275
Graph, directed      142
Graph, disconnected      286
Graph, distance regular      276
Graph, distance regular, imprimitive      280
Graph, distance regular, primitive      280
Graph, dual      101
Graph, Gewirtz      303
Graph, Higman — Sims      303
Graph, Hoffman — Singleton      296
Graph, McLaughlin      312
Graph, minimum distance      71 88
Graph, Moore      295
Graph, Paley      288
Graph, Petersen      296
Graph, planar      101
Graph, plane      71 89 100
Graph, regular      261
Graph, Schlaefli      292 312
Graph, Shrikhande      288
Graph, square lattice      287
Graph, strongly regular      286
Graph, strongly regular, complement      288
Graph, strongly regular, eigenvalue      289
Graph, strongly regular, Gewirtz      501
Graph, strongly regular, Hoffman — Singleton      506
Graph, strongly regular, McLaughlin      506 510
Graph, strongly regular, primitive      289
Graph, triangular      287
Graph, valency      261
Great-circle      443
Group automorphism      216
Group dihedral      207
Group representation      211
Group symmetry      205 344
Group transformation, distance preserving      219
Group transformation, orthogonal      207
Group, abelian, infinite      358
Group, alternant      10
Group, classical      307
Group, dihedral      227 234 252 253
Group, generating      206 220
Group, matrix, diagonal      218
Group, multiplicative, of diagonal matrices      224
Group, orbit of      344
Group, orthogonal      205 307
Group, reflection      207 213 230
Group, reflection, crystallographic      345
Group, reflection, finite      236 242 244
Group, reflection, geometrically equivalent      237
Group, reflection, irreducible      238 240 254
Group, symmetric      8 68 214 251
Hexagon      314
Hexagon, regular      68
Hypercube      262 325 328
Hyperplane, defining      243
Hyperplane, orthogonal      232
icosahedron      9 76 80 85 248 260 271 284 314 325 334
Idempotent, principal      265
Identities, Christoffel — Darboux      44 45 50 57
Identity, MacWilliams      223 226 228
Indicator matrix      257
Inequality, Cauchy      42
Inequality, Fisher      301
Inequality, Jensen's      84
Inequality, Schwarz'      244
Inequality, triangle      20
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте