Codes on Euclidean spheres:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam u.a.
Elsevier
2001
|
| Edition: | 1. ed. |
| Series: | North-Holland mathematical library
63 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 549 S. |
| ISBN: | 0444503293 |
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MARC
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| 245 | 1 | 0 | |a Codes on Euclidean spheres |c Thomas Ericson ; Victor Zinoviev |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Definitions and basic properties 1
1.2 Examples of spherical codes 5
1.3 Two basic functions 12
1.4 The Rankin bounds 14
1.5 The Simplex and the Biorthogonal codes 17
1.6 The Chabauty Shannon Wyner bound 19
1.7 The direct sum 24
2 The linear programming bound 27
2.1 Introduction 27
2.2 Spherical polynomials 28
2.3 The linear programming bound 39
2.4 Orthogonal polynomials 42
2.5 The Levenshtein bound 47
2.6 The Boyvalenkov Danev Bumova criterion 58
2.7 Properties of the Levenshtein bound 62
3 Codes in dimension n=3 67
3.1 Introduction 67
3.2 The optimal codes 68
3.3 Additional comments 79
3.4 The Fejes Toth bound 81
3.5 Optimality in the case M=7 86
3.6 The Coxeter Boroczky extension 97
3.7 Thirteen spheres 98
ix
4 Permutation codes 107
4.1 Introduction 107
4.2 Variant 1 108
4.3 Best variant 1 codes 113
4.4 Variant 2a 116
4.5 Variant 2b 119
4.6 Dimensionality 121
4.7 Decoding 123
4.8 General comments 126
5 Symmetric alphabets 129
5.1 Introduction 129
5.2 An introductory example 130
5.3 Binary labeling 134
5.4 The construction: 2 K 4 138
5.5 The construction: general case 142
5.6 A simple example 149
5.7 Analysis 151
5.8 Explicit constructions 156
5.9 Unions 161
5.10 Extensions 169
5.11 Concluding remarks 175
6 Non symmetric alphabets 179
6.1 Introduction 179
6.2 The binary balanced mapping 179
6.3 Comments 182
6.4 Unions from the CW^ construction 183
6.5 Non symmetric ternary alphabet 185
6.6 The general balanced construction 188
7 Polyphase codes 195
7.1 Introduction 195
7.2 General properties 195
7.3 The case q = 3 197
7.4 The case q = 4 199
7.5 The case q = 6 200
7.6 The case q = 8 200
7.7 Two special constructions 201
7.8 A general comment 202
8 Group codes 205
8.1 Introduction 205
8.2 Basic properties 206
8.3 Groups represented by matrices 210
8.4 Group codes in binary Hamming spaces 213
8.5 Group codes from binary codes 218
8.6 Dual codes and MacWilliams identity 223
8.7 Finite reflection groups 230
8.8 Codes from finite reflection groups 242
8.9 Examples 247
8.10 Remarks on some specific codes 252
9 Distance regular spherical codes 257
9.1 Introduction 257
9.2 Association schemes 263
9.3 Metric schemes 275
9.4 Strongly regular graphs 285
9.5 The absolute bound 311
9.6 Spherical designs 314
9.7 Regular polytopes 324
10 Lattices 337
10.1 Introduction 337
10.2 Lattices 337
10.3 The root lattices 344
10.4 Sphere packings and packing bounds 348
10.5 Sphere packings and codes 353
10.6 Lattices and codes 358
10.7 Expurgated constructions 362
10.8 The Leech lattice 365
10.9 Theta functions 367
10.10 Spherical codes from lattices 371
10.11 Theta functions for expurgated constructions .... 378
10.12 Unions of shells 382
11 Decoding 389
11.1 Introduction 389
11.2 The problem 390
11.3 Preliminaries 391
11.4 Generalized minimum distance decoding 395
11.5 The Chase decoder 400
11.6 Parallel decoding 404
11.7 Decoding F3 409
A Algebraic codes and designs 417
B Spheres in R 439
C Spherical geometry 443
D Tables 451
D.I Introduction 451
D.2 Notation 452
D.3 Spherical codes of dimension n = 3 455
D.4 Spherical codes of dimension n = 4 456
D.5 Spherical codes of dimension n = 5 456
D.6 Spherical codes of dimension n = 6 457
D.7 Spherical codes of dimension n = 7 460
D.8 Spherical codes of dimension n = 8 463
D.9 Spherical codes of dimension n = 9 465
D.10 Spherical codes of dimension n = 10 468
D.ll Spherical codes of dimension n = 11 472
D.12 Spherical codes of dimension n = 12 475
D.13 Spherical codes of dimension n = 13 477
D.14 Spherical codes of dimension n = 14 480
D.I5 Spherical codes of dimension n = 15 483
D.16 Spherical codes of dimension n = 16 485
D.17 Spherical codes of dimension n = 17 488
D.18 Spherical codes of dimension n = 18 492
D.19 Spherical codes of dimension n = 19 497
D.20 Spherical codes of dimension n = 20 501
D.21 Spherical codes of dimension n = 21 506
D.22 Spherical codes of dimension n = 22 508
D.23 Spherical codes of dimension n = 23 512
D.24 Spherical codes of dimension n = 24 517
Bibliography 519
Index 541
|
| any_adam_object | 1 |
| author | Ericson, Thomas Zinov'ev, Viktor A. |
| author_facet | Ericson, Thomas Zinov'ev, Viktor A. |
| author_role | aut aut |
| author_sort | Ericson, Thomas |
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| ctrlnum | (OCoLC)46641954 (DE-599)BVBBV014113988 |
| dewey-full | 511/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.6 |
| dewey-search | 511/.6 |
| dewey-sort | 3511 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
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| id | DE-604.BV014113988 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:57:53Z |
| institution | BVB |
| isbn | 0444503293 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009669883 |
| oclc_num | 46641954 |
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| owner | DE-91 DE-BY-TUM DE-703 |
| owner_facet | DE-91 DE-BY-TUM DE-703 |
| physical | XIII, 549 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Elsevier |
| record_format | marc |
| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Ericson, Thomas Verfasser aut Codes on Euclidean spheres Thomas Ericson ; Victor Zinoviev 1. ed. Amsterdam u.a. Elsevier 2001 XIII, 549 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 63 Sphere packings Kugelpackung (DE-588)4165929-6 gnd rswk-swf Kugelpackung (DE-588)4165929-6 s DE-604 Zinov'ev, Viktor A. Verfasser aut North-Holland mathematical library 63 (DE-604)BV000005206 63 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009669883&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ericson, Thomas Zinov'ev, Viktor A. Codes on Euclidean spheres North-Holland mathematical library Sphere packings Kugelpackung (DE-588)4165929-6 gnd |
| subject_GND | (DE-588)4165929-6 |
| title | Codes on Euclidean spheres |
| title_auth | Codes on Euclidean spheres |
| title_exact_search | Codes on Euclidean spheres |
| title_full | Codes on Euclidean spheres Thomas Ericson ; Victor Zinoviev |
| title_fullStr | Codes on Euclidean spheres Thomas Ericson ; Victor Zinoviev |
| title_full_unstemmed | Codes on Euclidean spheres Thomas Ericson ; Victor Zinoviev |
| title_short | Codes on Euclidean spheres |
| title_sort | codes on euclidean spheres |
| topic | Sphere packings Kugelpackung (DE-588)4165929-6 gnd |
| topic_facet | Sphere packings Kugelpackung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009669883&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005206 |
| work_keys_str_mv | AT ericsonthomas codesoneuclideanspheres AT zinovevviktora codesoneuclideanspheres |