UID:
almahu_9947363378802882
Umfang:
XXIV, 667 p.
,
online resource.
ISBN:
9789401138109
Serie:
Mathematics and Its Applications (Soviet Series), 58
Anmerkung:
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.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9781402003356
Sprache:
Englisch
DOI:
10.1007/978-94-011-3810-9
URL:
http://dx.doi.org/10.1007/978-94-011-3810-9
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