UID:
almahu_9947362993402882
Umfang:
XXIII, 417 p.
,
online resource.
ISBN:
9781461214786
Serie:
Springer Series in Statistics,
Anmerkung:
1 Introduction -- 1.1 Problems -- 2 Rao’s Inequalities and Improvements -- 2.1 Introduction -- 2.2 Rao’s Inequalities -- 2.3 Improvements on Rao’s Bounds for Strength 2 and 3 -- 2.4 Improvements on Rao’s Bounds for Arrays of Index Unity -- 2.5 Orthogonal Arrays with Two Levels -- 2.6 Concluding Remarks -- 2.7 Notes on Chapter 2 -- 2.8 Problems -- 3 Orthogonal Arrays and Galois Fields -- 3.1 Introduction -- 3.2 Bush’s Construction -- 3.3 Addelman and Kempthorne’s Construction -- 3.4 The Rao-Hamming Construction -- 3.5 Conditions for a Matrix -- 3.6 Concluding Remarks -- 3.7 Problems -- 4 Orthogonal Arrays and Error-Correcting Codes -- 4.1 An Introduction to Error-Correcting Codes -- 4.2 Linear Codes -- 4.3 Linear Codes and Linear Orthogonal Arrays -- 4.4 Weight Enumerators and Delsarte’s Theorem -- 4.5 The Linear Programming Bound -- 4.6 Concluding Remarks -- 4.7 Notes on Chapter 4 -- 4.8 Problems -- 5 Construction of Orthogonal Arrays from Codes -- 5.1 Extending a Code by Adding More Coordinates -- 5.2 Cyclic Codes -- 5.3 The Rao-Hamming Construction Revisited -- 5.4 BCH Codes -- 5.5 Reed-Solomon Codes -- 5.6 MDS Codes and Orthogonal Arrays of Index Unity -- 5.7 Quadratic Residue and Golay Codes -- 5.8 Reed-Muller Codes -- 5.9 Codes from Finite Geometries -- 5.10 Nordstrom-Robinson and Related Codes -- 5.11 Examples of Binary Codes and Orthogonal Arrays -- 5.12 Examples of Ternary Codes and Orthogonal Arrays -- 5.13 Examples of Quaternary Codes and Orthogonal Arrays -- 5.14 Notes on Chapter 5 -- 5.15 Problems -- 6 Orthogonal Arrays and Difference Schemes -- 6.1 Difference Schemes -- 6.2 Orthogonal Arrays Via Difference Schemes -- 6.3 Bose and Bush’s Recursive Construction -- 6.4 Difference Schemes of Index 2 -- 6.5 Generalizations and Variations -- 6.6 Concluding Remarks -- 6.7 Notes on Chapter 6 -- 6.8 Problems -- 7 Orthogonal Arrays and Hadamard Matrices -- 7.1 Introduction -- 7.2 Basic Properties of Hadamard Matrices -- 7.3 The Connection Between Hadamard Matrices and Orthogonal Arrays -- 7.4 Constructions for Hadamard Matrices -- 7.5 Hadamard Matrices of Orders up to 200 -- 7.6 Notes on Chapter 7 -- 7.7 Problems -- 8 Orthogonal Arrays and Latin Squares -- 8.1 Latin Squares and Orthogonal Latin Squares -- 8.2 Frequency Squares and Orthogonal Frequency Squares -- 8.3 Orthogonal Arrays from Pairwise Orthogonal Latin Squares -- 8.4 Concluding Remarks -- 8.5 Problems -- 9 Mixed Orthogonal Arrays -- 9.1 Introduction -- 9.2 The Rao Inequalities for Mixed Orthogonal Arrays -- 9.3 Constructing Mixed Orthogonal Arrays -- 9.4 Further Constructions -- 9.5 Notes on Chapter 9 -- 9.6 Problems -- 10 Further Constructions and Related Structures -- 10.1 Constructions Inspired by Coding Theory -- 10.2 The Juxtaposition Construction -- 10.3 The (u, u + ?) Construction -- 10.4 Construction X4 -- 10.5 Orthogonal Arrays from Union of Translates of a Linear Code -- 10.6 Bounds on Large Orthogonal Arrays -- 10.7 Compound Orthogonal Arrays -- 10.8 Orthogonal Multi-Arrays -- 10.9 Transversal Designs, Resilient Functions and Nets -- 10.10 Schematic Orthogonal Arrays -- 10.11 Problems -- 11 Statistical Application of Orthogonal Arrays -- 11.1 Factorial Experiments -- 11.2 Notation and Terminology -- 11.3 Factorial Effects -- 11.4 Analysis of Experiments Based on Orthogonal Arrays -- 11.5 Two-Level Fractional Factorials with a Defining Relation -- 11.6 Blocking for a 2k-n Fractional Factorial -- 11.7 Orthogonal Main-Effects Plans and Orthogonal Arrays -- 11.8 Robust Design -- 11.9 Other Types of Designs -- 11.10 Notes on Chapter 11 -- 11.11 Problems -- 12 Tables of Orthogonal Arrays -- 12.1 Tables of Orthogonal Arrays of Minimal Index -- 12.2 Description of Tables 12.1?12.3 -- 12.3 Index Tables -- 12.4 If No Suitable Orthogonal Array Is Available -- 12.5 Connections with Other Structures -- 12.6 Other Tables -- Appendix A: Galois Fields -- A.1 Definition of a Field -- A.2 The Construction of Galois Fields -- A.3 The Existence of Galois Fields -- A.4 Quadratic Residues in Galois Fields -- A.5 Problems -- Author Index.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9781461271581
Sprache:
Englisch
DOI:
10.1007/978-1-4612-1478-6
URL:
http://dx.doi.org/10.1007/978-1-4612-1478-6
