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 -- 3.3 Additional comments -- 3.4 The Fejes Tóth bound -- 3.5 Optimality in the case M=7 -- 3.6 The Coxeter-Böröczky extension -- 3.7 Thirteen spheres -- Chapter 4. Permutation codes -- 4.1 Introduction -- 4.2 Variant 1 -- 4.3 Best variant 1 codes -- 4.4 Variant 2a -- 4.5 Variant 2b -- 4.6 Dimensionality -- 4.7 Decoding -- 4.8 General comments -- Chapter 5. Symmetric alphabets -- 5.1 Introduction -- 5.2 An introductory example -- 5.3 Binary labeling -- 5.4 The construction. 2 K 4 -- 5.5 The construction: general case -- 5.6 A simple example -- 5.7 Analysis -- 5.8 Explicit constructions -- 5.9 Unions -- 5.10 Extensions -- 5.11 Concluding remarks -- Chapter 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 -- 8.5 Group codes from binary codes -- 8.6 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 -- 10.7 Expurgated constructions -- 10.8 The Leech lattice -- 10.9 Theta functions -- 10.10 Spherical codes from lattices -- 10.11 Theta function.