目录
 前辅文
 Preface
 Chapter 1. Introduction
 Chapter 2. Designs
  2.1. Incidence structures
  2.2. t-Designs
  2.3. Affine planes
  2.4. Symmetric designs
  2.5. Projective geometry
 Chapter 3. Automorphisms of Designs
  3.1. Group actions
  3.2. Automorphisms of symmetric designs
 Chapter 4. Introducing Difference Sets
  4.1. Definition and examples
  4.2. Difference sets and designs
  4.3. Integral group ring
  4.4. Equivalence
 Chapter 5. Bruck-Ryser-Chowla Theorem
  5.1. The BRC Theorem
  5.2. Proof of BRC for v odd
  5.3. Partial converse and extension of BRC
 Chapter 6. Multipliers
  6.1. Definition and examples
  6.2. Existence of numerical multipliers
  6.3. Multipliers fix sD
  6.4. Using multipliers
  6.5. Multipliers in non-cyclic groups
 Chapter 7. Necessary Group Conditions
  7.1. Intersection numbers
  7.2. Turyn’s exponent bound
  7.3. Dillon’s dihedral trick
 Chapter 8. Difference Sets from Geometry
  8.1. Singer difference sets
  8.2. Turyn’s construction
  8.3. McFarland difference sets
 Chapter 9. Families from Hadamard Matrices
  9.1. Hadamard matrices
  9.2. Paley-Hadamard family: v=4n−1
  9.3. Hadamard family: v=4n
 Chapter 10. Representation Theory
  10.1. Definitions and examples
  10.2. Equivalent representations
  10.3. Maschke’s Theorem
  10.4. Representations and difference sets
 Chapter 11. Group Characters
  11.1. Definitions and examples
  11.2. The Fundamental Theorem
  11.3. Proof of the Fundamental Theorem
  11.4. Characters and difference sets
  11.5. Character tables
 Chapter 12. Using Algebraic Number Theory
  12.1. Why algebraic number theory?
  12.2. Definitions and basic facts
  12.3. Seeking difference sets
  12.4. Proving Turyn’s exponent bound
 Chapter 13. Applications
  13.1. Binary sequences
  13.2. Imaging with coded masks
  13.3. Error correcting codes
  13.4. Quantum information and MUBs
 Appendix A. Background
 Appendix B. Notation
 Appendix C. Hints and Solutions to Selected Exercises
 Bibliography
 Index
 Index of Parameters
 前辅文
 Preface
 Chapter 1. Introduction
 Chapter 2. Designs
  2.1. Incidence structures
  2.2. t-Designs
  2.3. Affine planes
  2.4. Symmetric designs
  2.5. Projective geometry
 Chapter 3. Automorphisms of Designs
  3.1. Group actions
  3.2. Automorphisms of symmetric designs
 Chapter 4. Introducing Difference Sets
  4.1. Definition and examples
  4.2. Difference sets and designs
  4.3. Integral group ring
  4.4. Equivalence
 Chapter 5. Bruck-Ryser-Chowla Theorem
  5.1. The BRC Theorem
  5.2. Proof of BRC for v odd
  5.3. Partial converse and extension of BRC
 Chapter 6. Multipliers
  6.1. Definition and examples
  6.2. Existence of numerical multipliers
  6.3. Multipliers fix sD
  6.4. Using multipliers
  6.5. Multipliers in non-cyclic groups
 Chapter 7. Necessary Group Conditions
  7.1. Intersection numbers
  7.2. Turyn’s exponent bound
  7.3. Dillon’s dihedral trick
 Chapter 8. Difference Sets from Geometry
  8.1. Singer difference sets
  8.2. Turyn’s construction
  8.3. McFarland difference sets
 Chapter 9. Families from Hadamard Matrices
  9.1. Hadamard matrices
  9.2. Paley-Hadamard family: v=4n−1
  9.3. Hadamard family: v=4n
 Chapter 10. Representation Theory
  10.1. Definitions and examples
  10.2. Equivalent representations
  10.3. Maschke’s Theorem
  10.4. Representations and difference sets
 Chapter 11. Group Characters
  11.1. Definitions and examples
  11.2. The Fundamental Theorem
  11.3. Proof of the Fundamental Theorem
  11.4. Characters and difference sets
  11.5. Character tables
 Chapter 12. Using Algebraic Number Theory
  12.1. Why algebraic number theory?
  12.2. Definitions and basic facts
  12.3. Seeking difference sets
  12.4. Proving Turyn’s exponent bound
 Chapter 13. Applications
  13.1. Binary sequences
  13.2. Imaging with coded masks
  13.3. Error correcting codes
  13.4. Quantum information and MUBs
 Appendix A. Background
 Appendix B. Notation
 Appendix C. Hints and Solutions to Selected Exercises
 Bibliography
 Index
 Index of Parameters