Codes on Euclidean Spheres
T. Ericson, V. Zinoviev
Elsevier, Apr 27, 2001 - Mathematics - 564 pages
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.
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Chapter 10 Lattices
Chapter 11 Decoding
Appendix A Algebraic codes and designs
Appendix B Spheres in R n
Appendix C Spherical geometry
Appendix D Tables
Chapter 9 Distance regular spherical codes