UID:
almahu_9947367532202882
Format:
1 online resource (565 p.)
Edition:
1st ed.
ISBN:
1-281-05005-9
,
9786611050054
,
0-08-050216-4
,
0-585-47385-4
Series Statement:
North-Holland mathematical library, v. 63
Content:
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 r
Note:
Description based upon print version of record.
,
Cover; Contents; Chapter 1. Introduction; 1.1 Definitions and basic properties; 1.2 Examples of spherical codes; 1.3 Two basic functions; 1.4 The Rankin bounds; 1.5 The Simplex and the Biorthogonal codes; 1.6 The Chabauty-Shannon-Wyner bound; 1.7 The direct sum; Chapter 2. The linear programming bound; 2.1 Introduction; 2.2 Spherical polynomials; 2.3 The linear programming bound; 2.4 Orthogonal polynomials; 2.5 The Levenshtein bound; 2.6 The Boyvalenkov-Danev-Bumova criterion; 2.7 Properties of the Levenshtein bound; Chapter 3. Codes in dimension n=3; 3.1 Introduction; 3.2 The optimal codes
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5.11 Concluding remarksChapter 6. Non-symmetric alphabets; 6.1 Introduction; 6.2 The binary balanced mapping; 6.3 Comments; 6.4 Unions from the CW2-construction; 6.5 Non-symmetric ternary alphabet; 6.6 The general balanced construction; Chapter 7. Polyphase codes; 7.1 Introduction; 7.2 General properties; 7.3 The case q = 3; 7.4 The case q = 4; 7.5 The case q = 6; 7.6 The case q = 8; 7.7 Two special constructions; 7. 8 A general comment; Chapter 8. Group codes; 8.1 Introduction; 8.2 Basic properties; 8.3 Groups represented by matrices; 8.4 Group codes in binary Hamming spaces
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8.5 Group codes from binary codes8.6 Dual codes and MacWilliams' identity; 8.7 Finite reflection groups; 8.8 Codes from finite reflection groups; 8.9 Examples; 8.10 Remarks on some specific codes; Chapter 9. Distance regular spherical codes; 9.1 Introduction; 9.2 Association schemes; 9.3 Metric schemes; 9.4 Strongly regular graphs; 9.5 The absolute bound; 9.6 Spherical designs; 9.7 Regular polytopes; Chapter 10. Lattices; 10.1 Introduction; 10.2 Lattices; 10.3 The root lattices; 10.4 Sphere packings and packing bounds; 10.5 Sphere packings and codes; 10.6 Lattices and codes
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10.7 Expurgated constructions10.8 The Leech lattice; 10.9 Theta functions; 10.10 Spherical codes from lattices; 10.11 Theta functions for expurgated constructions; 10.12 Unions of shells; Chapter 11. Decoding; 11.1 Introduction; 11.2 The problem; 11.3 Preliminaries; 11.4 Generalized minimum distance decoding; 11.5 The Chase decoder; 11.6 Parallel decoding; 11.7 Decoding Y3; Appendix A. Algebraic codes and designs; Appendix B. Spheres in R n; Appendix C. Spherical geometry; Appendix D. Tables; D.1 Introduction; D.2 Notation; D.3 Spherical codes of dimension n = 3
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D.4 Spherical codes of dimension n = 4
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English
Additional Edition:
ISBN 0-444-50329-3
Language:
English
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