Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. Mathematically the topic belongs to the realm of algebraic combinatorics, with close connections to number theory, geometry, combinatorial theory, and - of course - to algebraic coding theory. The connections to physics occur within areas like crystallography and nuclear physics. In engineering spherical codes are of central importance in connection with error-control in communication systems. In that context the use of spherical codes is often referred to as "coded modulation." The book offers a first complete treatment of the mathematical theory of codes on Euclidean spheres. Many new results are published here for the first time. Engineering applications are emphasized throughout the text. The theory is illustrated by many examples. The book also contains an extensive table of best known spherical codes in dimensions 3-24, including exact constructions.
Table of Contents
1. Introduction 2. The linear programming bound 3. Codes in dimension n=3 4. Permutation codes 5. Symmetric alphabets 6. Non-symmetric alphabets 7. Polyphase codes 8. Group codes 9. Distance regular spherical codes 10. Lattices 11. Decodin
Appendix: A Algebraic codes and designs B Spheres in R n C Spherical geometry D Tables