Algebraic function fields and codes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1993
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 260 S. |
| ISBN: | 3540564896 0387564896 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804121808640671744 |
|---|---|
| adam_text | Contents
Chapter I. Foundations of the Theory
of Algebraic Function Fields 1
1.1 Places 1
1.2 The Rational Function Field 8
1.3 Independence of Valuations 11
1.4 Divisors 14
1.5 The Riemann Roch Theorem 22
1.6 Some Consequences of the Riemann Roch Theorem 29
1.7 Local Components of Weil Differentials 35
Chapter II. Geometric Goppa Codes 39
II. 1 Codes 39
11.2 Geometric Goppa Codes 42
11.3 Geometric Goppa Codes Associated with the
Rational Function Field 49
Chapter III. Extensions of Algebraic Function Fields 58
111.1 Algebraic Extensions of Function Fields 59
111.2 Subrings of Function Fields 67
111.3 Local Integral Bases 71
111.4 The Cotrace of Weil Differentials and the
Hurwitz Genus Formula 80
111.5 The Different 89
111.6 Constant Field Extensions 101
111.7 Galois Extensions I 109
111.8 Galois Extensions II 118
111.9 Inseparable Extensions 127
III. 10 Estimates for the Genus of a Function Field 129
Chapter IV. Differentials of Algebraic Function Fields 134
IV.l Derivations and Differentials 134
IV.2 The P adic Completion 140
IV.3 Differentials and Weil Differentials 148
X Contents
Chapter V. Algebraic Function Fields
over Finite Constant Fields 158
V.I The Zeta Function of a Function Field 158
V.2 The Hasse Weil Theorem 169
V.3 Improvements of the Hasse Weil Bound 180
Chapter VI. Examples of Algebraic Function Fields 186
VI. 1 Elliptic Function Fields 186
VI.2 Hyperelliptic Function Fields 193
VI.3 Tame Cyclic Extensions of the Rational Function Field 196
VI.4 Some Elementary Abelian p Extensions of K(x),
char K = p 0 200
Chapter VII. More about Geometric Goppa Codes 204
VII.l The Residue Representation of Cn(D, G) 204
VII.2 Long Codes 205
VII.3 Automorphisms 209
VII.4 Hermitian Codes 211
VII.5 Decoding Geometric Goppa Codes 215
Chapter VIII. Subfleld Subcodes and Trace Codes 221
VIII. 1 On the Dimension of Subfield Subcodes and Trace Codes 221
VIII.2 Weights of Trace Codes 225
Appendix A. Field Theory 235
Appendix B. Algebraic Curves and Algebraic Function Fields 242
Bibliography 251
List of Notation 253
Index 257
|
| any_adam_object | 1 |
| author | Stichtenoth, Henning 1944- |
| author_GND | (DE-588)141456280 |
| author_facet | Stichtenoth, Henning 1944- |
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| classification_tum | MAT 125f DAT 584f |
| ctrlnum | (OCoLC)246555658 (DE-599)BVBBV007517674 |
| dewey-full | 512/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:03:52Z |
| institution | BVB |
| isbn | 3540564896 0387564896 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004893054 |
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| physical | X, 260 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Stichtenoth, Henning 1944- Verfasser (DE-588)141456280 aut Algebraic function fields and codes Henning Stichtenoth Berlin [u.a.] Springer 1993 X, 260 S. txt rdacontent n rdamedia nc rdacarrier Universitext Corps algébriques Fonctions algébriques Funcoes algebricas larpcal Algebraic fields Algebraic functions Algebraische Funktion (DE-588)4141836-0 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Fehlerkorrekturcode (DE-588)4124917-3 gnd rswk-swf Algebraischer Funktionenkörper (DE-588)4141850-5 gnd rswk-swf Algebraischer Funktionenkörper (DE-588)4141850-5 s Fehlerkorrekturcode (DE-588)4124917-3 s DE-604 Algebraische Funktion (DE-588)4141836-0 s Codierungstheorie (DE-588)4139405-7 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004893054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stichtenoth, Henning 1944- Algebraic function fields and codes Corps algébriques Fonctions algébriques Funcoes algebricas larpcal Algebraic fields Algebraic functions Algebraische Funktion (DE-588)4141836-0 gnd Codierungstheorie (DE-588)4139405-7 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd |
| subject_GND | (DE-588)4141836-0 (DE-588)4139405-7 (DE-588)4124917-3 (DE-588)4141850-5 |
| title | Algebraic function fields and codes |
| title_auth | Algebraic function fields and codes |
| title_exact_search | Algebraic function fields and codes |
| title_full | Algebraic function fields and codes Henning Stichtenoth |
| title_fullStr | Algebraic function fields and codes Henning Stichtenoth |
| title_full_unstemmed | Algebraic function fields and codes Henning Stichtenoth |
| title_short | Algebraic function fields and codes |
| title_sort | algebraic function fields and codes |
| topic | Corps algébriques Fonctions algébriques Funcoes algebricas larpcal Algebraic fields Algebraic functions Algebraische Funktion (DE-588)4141836-0 gnd Codierungstheorie (DE-588)4139405-7 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd |
| topic_facet | Corps algébriques Fonctions algébriques Funcoes algebricas Algebraic fields Algebraic functions Algebraische Funktion Codierungstheorie Fehlerkorrekturcode Algebraischer Funktionenkörper |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004893054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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