عنوان

Algebraic-Geometric Codes

(Number (ISBN

9781402003356

(Number (ISBN

9789401138109

Number

dltt

Title Proper

Algebraic-Geometric Codes

General Material Designation

[Book]

First Statement of Responsibility

by M. A. Tsfasman, S. G. Vlǎduţ.

Place of Publication, Distribution, etc.

Dordrecht :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

1991.

Series Title

Mathematics and Its Applications (Soviet Series),

Volume Designation

58

ISSN of Series

0169-6378 ;

Text of Note

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.

0

Text of Note

'Et moi, ... , si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d' etre of this series.

International Standard Book Number

9781402003356

Title

Springer eBooks

Computer engineering.

Geometry, Algebraic.

Information theory.

Mathematics.

Number theory.

Tsfasman, M. A.

Vlǎduţ, S. G.

SpringerLink (Online service)

Date of Transaction

20190301073800.0

Electronic name

[Book]

Y