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Algebraic-Geometric Codes
Michael A. Tsfasman,S.G. Vladut +1 more
- 30 Apr 1991
659
TL;DR: In this article, an AG-Codes and their parameters and constructions are compared with those of binary codes from AG-codes, as well as asymptotic bounds.
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Abstract: 1 Codes- 11 Codes and their parameters- 12 Examples and constructions- 13 Asymptotic problems- 2 Curves- 21 Algebraic curves- 22 Riemann-Roch theorem- 23 Rational points- 24 Elliptic curves- 25 Singular curves- 26 Reductions and schemes- 3 AG-Codes- 31 Constructions and properties- 32 Examples- 33 Decoding- 34 Asymptotic results- 4 Modular Codes- 41 Codes on classical modular curves- 42 Codes on Drinfeld curves- 43 Polynomiality- 5 Sphere Packings- 51 Definitions and examples- 52 Asymptotically dense packings- 53 Number fields- 54 Analogues of AG-codes- Appendix Summary of results and tables- A1 Codes of finite length- A11 Bounds- A12 Parameters of certain codes- A13 Parameters of certain constructions- A14 Binary codes from AG-codes- A2 Asymptotic bounds- A21 List of bounds- A22 Diagrams of comparison- A23 Behaviour at the ends- A24 Numerical values- A3 Additional bounds- A31 Constant weight codes- A32 Self-dual codes- A4 Sphere packings- A41 Small dimensions- A42 Certain families- A43 Asymptotic results- Author index- List of symbols
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Sphere-bound-achieving coset codes and multilevel coset codes
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Geometric approach to higher weights
Michael A. Tsfasman,S.G. Vladut +1 more
TL;DR: The notion of higher (or generalized) weights of codes is just as natural as that of the classical Hamming weight and the authors adopt the geometric point of view.
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