Table of Contents:
- Front Cover; Dedication ; Galois Fields and Galois Rings Made Easy; Copyright ; Contents; Acknowledgments; Preface; List of Mathematical Symbols; Sets; Numbers; Matrices; Groups; Rings; Fields; 1. The Structures of Ring and Field; 1.1. Rings; 1.2. Fields; 2. Galois Fields; 2.1. Generalities; 2.2. Extension of a field: a typical example; 2.3. Extension of a field: the general case; 2.4. Sub-field of a Galois field; 2.5. Factorizations; 2.6. The application trace for a Galois field; 2.7. Bases of a Galois field; 2.8. Characters of a Galois field; 2.9. Gaussian sums over Galois fields.
- 3. Galois Rings3.1. Generalities; 3.2. Construction of a Galois ring; 3.3. Examples and counter-examples of Galois rings; 3.4. The application trace for a Galois ring; 3.5. Characters of a Galois ring; 3.6. Gaussian sums over Galois rings; 4. Mutually Unbiased Bases; 4.1. Generalities; 4.2. Quantum angular momentum bases; 4.3. SU(2) approach to mutually unbiased bases; 4.4. Galois field approach to mutually unbiased bases; 4.5. Galois ring approach to mutually unbiased bases; 5. Appendix on Number Theory and Group Theory; 5.1. Elements of number theory; 5.2. Elements of group theory.