Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorHedayat, A. S. author
TitleOrthogonal Arrays [electronic resource] : Theory and Applications / by A. S. Hedayat, N. J. A. Sloane, John Stufken
ImprintNew York, NY : Springer New York : Imprint: Springer, 1999
Connect tohttp://dx.doi.org/10.1007/978-1-4612-1478-6
Descript XXIII, 417 p. online resource

CONTENT

1 Introduction -- 1.1 Problems -- 2 Raoโ{128}{153}s Inequalities and Improvements -- 2.1 Introduction -- 2.2 Raoโ{128}{153}s Inequalities -- 2.3 Improvements on Raoโ{128}{153}s Bounds for Strength 2 and 3 -- 2.4 Improvements on Raoโ{128}{153}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 Bushโ{128}{153}s Construction -- 3.3 Addelman and Kempthorneโ{128}{153}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 Delsarteโ{128}{153}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 Bushโ{128}{153}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


Mathematics Probabilities Statistics Mathematics Probability Theory and Stochastic Processes Statistical Theory and Methods



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram