Research Catalog

Title

Algebraic function fields and codes / Henning Stichtenoth.

Author

Stichtenoth, H. (Henning), 1944-

Publication

Berlin ; New York : Springer-Verlag, 1993.

Items in the Library & Off-site

Details

Description

x, 260 pages; 24 cm.

Series Statement

Universitext.

Uniform Title

Universitext.

Subject

• Algebraic functions
• Algebraic fields
• 31.14 number theory
• Algebraische Funktion
• Algebraischer Funktionenkörper
• Fehlerkorrekturcode
• Funcoes algebricas

Bibliography (note)

• Includes bibliographical references (p. [251]-252) and index.

Contents

Ch. I. Foundations of the Theory of Algebraic Function Fields -- I.1. Places -- I.2. The Rational Function Field -- I.3. Independence of Valuations -- I.4. Divisors -- I.5. The Riemann-Roch Theorem -- I.6. Some Consequences of the Riemann-Roch Theorem -- I.7. Local Components of Weil Differentials -- Ch. II. Geometric Goppa Codes -- II. 1. Codes -- II. 2. Geometric Goppa Codes -- II. 3. Geometric Goppa Codes Associated with the Rational Function Field -- Ch. III. Extensions of Algebraic Function Fields -- III. 1. Algebraic Extensions of Function Fields -- III. 2. Subrings of Function Fields -- III. 3. Local Integral Bases -- III. 4. The Cotrace of Weil Differentials and the Hurwitz Genus Formula -- III. 5. The Different -- III. 6. Constant Field Extensions -- III. 7. Galois Extensions I -- III. 8. Galois Extensions II -- III. 9. Inseparable Extensions -- III. 10. Estimates for the Genus of a Function Field -- Ch. IV. Differentials of Algebraic Function Fields -- IV. 1. Derivations and Differentials -- IV. 2. The P-adic Completion -- IV. 3. Differentials and Weil Differentials -- Ch. V. Algebraic Function Fields over Finite Constant Fields -- V.1. The Zeta Function of a Function Field -- V.2. The Hasse-Weil Theorem -- V.3. Improvements of the Hasse-Weil Bound -- Ch. VI. Examples of Algebraic Function Fields -- VI. 1. Elliptic Function Fields -- VI. 2. Hyperelliptic Function Fields -- VI. 3. Tame Cyclic Extensions of the Rational Function Field -- VI. 4. Some Elementary Abelian p-Extensions of K(x), char K = p> 0 -- Ch. VII. More about Geometric Goppa Codes -- VII. 1. The Residue Representation of C[subscript Omega](D, G) -- VII. 2. Long Codes -- VII. 3. Automorphisms -- VII. 4. Hermitian Codes -- VII. 5. Decoding Geometric Goppa Codes -- Ch. VIII. Subfield Subcodes and Trace Codes -- VIII. 1. On the Dimension of Subfield Subcodes and Trace Codes -- VIII. 2. Weights of Trace Codes. Appendix A. Field Theory -- Appendix B. Algebraic Curves and Algebraic Function Fields.

ISBN

• 0387564896
• 9780387564890
• 3540564896
• 9783540564898

LCCN

93007182

OCLC

• ocm27727330
• 27727330
• SCSB-1991261

Owning Institutions

Princeton University Library