Codes on Euclidean Spheres

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T. Ericson, V. Zinoviev
Elsevier, Apr 27, 2001 - Mathematics - 564 pages
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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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Contents

Chapter 1 Introduction
1
Chapter 2 The linear programming bound
27
Chapter 3 Codes in dimension n3
67
Chapter 4 Permutation codes
107
Chapter 5 Symmetric alphabets
129
Chapter 6 Nonsymmetric alphabets
179
Chapter 7 Polyphase codes
195
Chapter 8 Group codes
205
Chapter 10 Lattices
337
Chapter 11 Decoding
389
Appendix A Algebraic codes and designs
417
Appendix B Spheres in R n
439
Appendix C Spherical geometry
443
Appendix D Tables
451
Bibliography
519
Index
541

Chapter 9 Distance regular spherical codes
257

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Page 535 - A New Multilevel Coding Method Using Error Correcting Codes," IEEE Trans, on Information Theory, Vol. IT-23, No. 3, pp. 371-376, May 1977. 5. VV Ginzburg, "Multidimensional Signals for a Continuous Channel," Problemy Peredachi Informatsii, Vol. 20, No. 1, pp. 28-46, 1984. 6. SI Sayegh, "A Class of Optimum Block Codes in Signal Space," IEEE Trans, on Communications, Vol.
Page 535 - Analytical treatment of the polytopes regularly derived from the regular polytopes", Ver.
Page 520 - E. Bannai, Spherical i-designs which are orbits of finite groups, J. Math. Soc. Japan, Vol. 36, pp.
Page 537 - VM Sidelnikov, Orbital spherical 11-designs whose initial point is a root of an invariant polynomial, St.

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