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＜電子ブック＞
Algebraic-Geometric Codes / by M. Tsfasman, S.G. Vladut
(Mathematics and its Applications, Soviet Series ; 58)

版	1st ed. 1991.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1991
本文言語	英語
大きさ	XXIV, 667 p : online resource
著者標目	*Tsfasman, M author Vladut, S.G author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Number theory LCSH:Electrical engineering LCSH:Computer science FREE:Algebraic Geometry FREE:Number Theory FREE:Electrical and Electronic Engineering FREE:Theory of Computation
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-94-011-3810-9

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