Algebraic-Geometric Codes [Paperback]

1. Codes.- 1.1. Codes and their parameters.- 1.2. Examples and constructions.- 1.3. Asymptotic problems.- 2. Curves.- 2.1. Algebraic curves.- 2.2. Riemann-Roch theorem.- 2.3. Rational points.- 2.4. Elliptic curves.- 2.5. Singular curves.- 2.6. Reductions and schemes.- 3. AG-Codes.- 3.1. Constructions and properties.- 3.2. Examples.- 3.3. Decoding.- 3.4. Asymptotic results.- 4. Modular Codes.- 4.1. Codes on classical modular curves.- 4.2. Codes on Drinfeld curves.- 4.3. Polynomiality.- 5. Sphere Packings.- 5.1. Definitions and examples.- 5.2. Asymptotically dense packings.- 5.3. Number fields.- 5.4. Analogues of AG-codes.- Appendix. Summary of results and tables.- A.1. Codes of finite length.- A.1.1. Bounds.- A.1.2. Parameters of certain codes.- A.1.3. Parameters of certain constructions.- A.1.4. Binary codes from AG-codes.- A.2. Asymptotic bounds.- A.2.1. List of bounds.- A.2.2. Diagrams of comparison.- A.2.3. Behaviour at the ends.- A.2.4. Numerical values.- A.3. Additional bounds.- A.3.1. Constant weight codes.- A.3.2. Self-dual codes.- A.4. Sphere packings.- A.4.1. Small dimensions.- A.4.2. Certain families.- A.4.3. Asymptotic results.- Author index.- List of symbols.Springer Book Archives