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Orthogonal arrays: theory and applications

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Bibliographic Details
Main Authors:	Hedayat, Abdossamad 1937- (Author), Sloane, Neil J. A. 1939- (Author), Stufken, John (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Springer 1999
Series:	Springer series in statistics
Subjects:	Orthogonales Array Orthogonal arrays Versuchsplanung Orthogonalität
Online Access:	Inhaltsverzeichnis
Physical Description:	XXII, 416 S.
ISBN:	0387987665

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MARC


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Record in the Search Index

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adam_text	A.S. HEDAYAT NJ.A. SLOANE JOHN STUFKEN ORTHOGONAL ARRAYS THEORY AND APPLICATIONS SPRINGER CONTENTS PREFACE VII FOREWORD BY C. R. RAO XV LIST OF SYMBOLS XXIII 1 INTRODUCTION 1 1.1 PROBLEMS 8 2 RAO S INEQUALITIES AND IMPROVEMENTS 11 2.1 INTRODUCTION 11 2.2 RAO S INEQUALITIES 12 2.3 IMPROVEMENTS ON RAO S BOUNDS FOR STRENGTH 2 AND 3 17 2.4 IMPROVEMENTS ON RAO S BOUNDS FOR ARRAYS OF INDEX UNITY .... 22 2.5 ORTHOGONAL ARRAYS WITH TWO LEVELS 27 2.6 CONCLUDING REMARKS 32 2.7 NOTES ON CHAPTER 2 33 2.8 PROBLEMS 33 3 ORTHOGONAL ARRAYS AND GALOIS FIELDS 37 3.1 INTRODUCTION 37 XVII XVIII CONTENTS 3.2 BUSH S CONSTRUCTION 38 3.3 ADDELMAN AND KEMPTHORNE S CONSTRUCTION 44 3.4 THE RAO-HAMMING CONSTRUCTION 49 3.5 CONDITIONS FOR A MATRIX 54 3.6 CONCLUDING REMARKS 56 3.7 PROBLEMS 56 4 ORTHOGONAL ARRAYS AND ERROR-CORRECTING CODES 61 4.1 AN INTRODUCTION TO ERROR-CORRECTING CODES 61 4.2 LINEAR CODES 63 4.3 LINEAR CODES AND LINEAR ORTHOGONAL ARRAYS 65 4.4 WEIGHT ENUMERATORS AND DELSARTE S THEOREM 67 4.5 THE LINEAR PROGRAMMING BOUND 72 4.6 CONCLUDING REMARKS 82 4.7 NOTES ON CHAPTER 4 82 4.8 PROBLEMS 85 5 CONSTRUCTION OF ORTHOGONAL ARRAYS FROM CODES 87 5.1 EXTENDING A CODE BY ADDING MORE COORDINATES 87 5.2 CYCLIC CODES 88 5.3 THE RAO-HAMMING CONSTRUCTION REVISITED 91 5.4 BCH CODES 93 5.5 REED-SOLOMON CODES 95 5.6 MDS CODES AND ORTHOGONAL ARRAYS OF INDEX UNITY 96 5.7 QUADRATIC RESIDUE AND GOLAY CODES 99 5.8 REED-MULLER CODES /. 99 5.9 CODES FROM FINITE GEOMETRIES 101 CONTENTS XIX 5.10 NORDSTROM-ROBINSON AND RELATED CODES 102 5.11 EXAMPLES OF BINARY CODES AND ORTHOGONAL ARRAYS 103 5.12 EXAMPLES OF TERNARY CODES AND ORTHOGONAL ARRAYS 105 5.13 EXAMPLES OF QUATERNARY CODES AND ORTHOGONAL ARRAYS 106 5.14 NOTES ON CHAPTER 5 108 5.15 PROBLEMS 109 6 ORTHOGONAL ARRAYS AND DIFFERENCE SCHEMES 113 6.1 DIFFERENCE SCHEMES 113 6.2 ORTHOGONAL ARRAYS VIA DIFFERENCE SCHEMES 118 6.3 BOSE AND BUSH S RECURSIVE CONSTRUCTION 123 6.4 DIFFERENCE SCHEMES OF INDEX 2 127 6.5 GENERALIZATIONS AND VARIATIONS 132 6.6 CONCLUDING REMARKS 138 6.7 NOTES ON CHAPTER 6 140 6.8 PROBLEMS 141 7 ORTHOGONAL ARRAYS AND HADAMARD MATRICES 145 7.1 INTRODUCTION 145 7.2 BASIC PROPERTIES OF HADAMARD MATRICES 146 7.3 THE CONNECTION BETWEEN HADAMARD MATRICES AND ORTHOGONAL ARRAYS 148 7.4 CONSTRUCTIONS FOR HADAMARD MATRICES 148 7.5 HADAMARD MATRICES OF ORDERS UP TO 200 155 7.6 NOTES ON CHAPTER 7 163 7.7 PROBLEMS 165 8 ORTHOGONAL ARRAYS AND LATIN SQUARES 167 XX CONTENTS 8.1 LATIN SQUARES AND ORTHOGONAL LATIN SQUARES 168 8.2 FREQUENCY SQUARES AND ORTHOGONAL FREQUENCY SQUARES 173 8.3 ORTHOGONAL ARRAYS FROM PAIRWISE ORTHOGONAL LATIN SQUARES . . . 183 8.4 CONCLUDING REMARKS 191 8.5 PROBLEMS 196 9 MIXED ORTHOGONAL ARRAYS 199 9.1 INTRODUCTION 199 9.2 THE RAO INEQUALITIES FOR MIXED ORTHOGONAL ARRAYS 201 9.3 CONSTRUCTING MIXED ORTHOGONAL ARRAYS 203 9.4 FURTHER CONSTRUCTIONS 211 9.5 NOTES ON CHAPTER 9 219 9.6 PROBLEMS 220 10 FURTHER CONSTRUCTIONS AND RELATED STRUCTURES 223 10.1 CONSTRUCTIONS INSPIRED BY CODING THEORY 223 10.2 THE JUXTAPOSITION CONSTRUCTION 224 10.3 THE (IT, U + V) CONSTRUCTION 225 10.4 CONSTRUCTION X4 226 10.5 ORTHOGONAL ARRAYS FROM UNION OF TRANSLATES OF A LINEAR CODE . . 228 10.6 BOUNDS ON LARGE ORTHOGONAL ARRAYS 228 10.7 COMPOUND ORTHOGONAL ARRAYS 230 10.8 ORTHOGONAL MULTI-ARRAYS 236 10.9 TRANSVERSAL DESIGNS, RESILIENT FUNCTIONS AND NETS 242 10.10 SCHEMATIC ORTHOGONAL ARRAYS 245 10.11 PROBLEMS 246 11 STATISTICAL APPLICATION OF ORTHOGONAL ARRAYS 247 CONTENTS XXI 11.1 FACTORIAL EXPERIMENTS 247 11.2 NOTATION AND TERMINOLOGY 249 11.3 FACTORIAL EFFECTS 251 11.4 ANALYSIS OF EXPERIMENTS BASED ON ORTHOGONAL ARRAYS 258 11.5 TWO-LEVEL FRACTIONAL FACTORIALS WITH A DENNING RELATION 272 11.6 BLOCKING FOR A 2 K ~ N FRACTIONAL FACTORIAL 282 11.7 ORTHOGONAL MAIN-EFFECTS PLANS AND ORTHOGONAL ARRAYS 288 11.8 ROBUST DESIGN 298 11.9 OTHER TYPES OF DESIGNS 302 11.10 NOTES ON CHAPTER 11 305 11.11 PROBLEMS 308 12 TABLES OF ORTHOGONAL ARRAYS 317 12.1 TABLES OF ORTHOGONAL ARRAYS OF MINIMAL INDEX 317 12.2 DESCRIPTION OF TABLES 12.1-12.3 318 12.3 INDEX TABLES 324 12.4 IF NO SUITABLE ORTHOGONAL ARRAY IS AVAILABLE 336 12.5 CONNECTIONS WITH OTHER STRUCTURES 338 12.6 OTHER TABLES 339 APPENDIX A: GALOIS FIELDS 341 A.I DEFINITION OF A FIELD 341 A.2 THE CONSTRUCTION OF GALOIS FIELDS 344 A.3 THE EXISTENCE OF GALOIS FIELDS 351 A.4 QUADRATIC RESIDUES IN GALOIS FIELDS 357 A.5 PROBLEMS 359 BIBLIOGRAPHY 363 XXII CONTENTS AUTHOR INDEX 406 SUBJECT INDEX 411
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author	Hedayat, Abdossamad 1937- Sloane, Neil J. A. 1939- Stufken, John
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spelling	Hedayat, Abdossamad 1937- Verfasser (DE-588)172153433 aut Orthogonal arrays theory and applications A. S. Hedayat ; N. J. A. Sloane ; John Stufken New York [u.a.] Springer 1999 XXII, 416 S. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Orthogonales Array Orthogonal arrays Versuchsplanung (DE-588)4078859-3 gnd rswk-swf Orthogonales Array (DE-588)4560879-9 gnd rswk-swf Orthogonalität (DE-588)4139058-1 gnd rswk-swf Versuchsplanung (DE-588)4078859-3 s Orthogonalität (DE-588)4139058-1 s DE-604 Orthogonales Array (DE-588)4560879-9 s Sloane, Neil J. A. 1939- Verfasser (DE-588)121291553 aut Stufken, John Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008620297&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Hedayat, Abdossamad 1937- Sloane, Neil J. A. 1939- Stufken, John Orthogonal arrays theory and applications Orthogonales Array Orthogonal arrays Versuchsplanung (DE-588)4078859-3 gnd Orthogonales Array (DE-588)4560879-9 gnd Orthogonalität (DE-588)4139058-1 gnd
subject_GND	(DE-588)4078859-3 (DE-588)4560879-9 (DE-588)4139058-1
title	Orthogonal arrays theory and applications
title_auth	Orthogonal arrays theory and applications
title_exact_search	Orthogonal arrays theory and applications
title_full	Orthogonal arrays theory and applications A. S. Hedayat ; N. J. A. Sloane ; John Stufken
title_fullStr	Orthogonal arrays theory and applications A. S. Hedayat ; N. J. A. Sloane ; John Stufken
title_full_unstemmed	Orthogonal arrays theory and applications A. S. Hedayat ; N. J. A. Sloane ; John Stufken
title_short	Orthogonal arrays
title_sort	orthogonal arrays theory and applications
title_sub	theory and applications
topic	Orthogonales Array Orthogonal arrays Versuchsplanung (DE-588)4078859-3 gnd Orthogonales Array (DE-588)4560879-9 gnd Orthogonalität (DE-588)4139058-1 gnd
topic_facet	Orthogonales Array Orthogonal arrays Versuchsplanung Orthogonalität
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008620297&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT hedayatabdossamad orthogonalarraystheoryandapplications AT sloaneneilja orthogonalarraystheoryandapplications AT stufkenjohn orthogonalarraystheoryandapplications

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