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- catalog contributor b4582422.
- catalog created "1993.".
- catalog date "1993".
- catalog date "1993.".
- catalog dateCopyrighted "1993.".
- catalog description "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.".
- catalog description "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.".
- catalog description "Includes bibliographical references (p.[251]-252) and index.".
- catalog description "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.".
- catalog extent "x, 260 p. :".
- catalog identifier "0387564896".
- catalog isPartOf "Universitext".
- catalog issued "1993".
- catalog issued "1993.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog subject "512/.74 20".
- catalog subject "Algebraic fields.".
- catalog subject "Algebraic functions.".
- catalog subject "QA341 .S75 1993".
- catalog tableOfContents "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.".
- catalog tableOfContents "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.".
- catalog tableOfContents "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.".
- catalog title "Algebraic function fields and codes / Henning Stichtenoth.".
- catalog type "text".