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Bibliographic Details
Other Authors:	Stichtenoth, Henning 1944- (Editor)
Format:	Electronic eBook
Language:	English
Published:	Berlin ; Heidelberg Springer 2009
Edition:	second edition
Series:	Graduate texts in mathematics 254
Subjects:	Algebraische Funktion Fehlerkorrekturcode Codierungstheorie Algebraischer Funktionenkörper
Online Access:	BTU01 TUM01 UBA01 UBM01 UBT01 UER01 UPA01 Volltext Inhaltsverzeichnis
Physical Description:	1 Online-Ressource
ISBN:	9783540768784
DOI:	10.1007/978-3-540-76878-4

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Record in the Search Index

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adam_text	CONTENTS 1 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 12 1.4 DIVISORS 15 1.5 THE RIEMANN-ROCH THEOREM 24 1.6 SOME CONSEQUENCES OF THE RIEMANN-ROCH THEOREM 31 1.7 LOCAL COMPONENTS OF WEIL DIFFERENTIALS 37 1.8 EXERCISES 40 2 ALGEBRAIC GEOMETRY CODES 45 2.1 CODES 45 2.2 AG CODES 48 2.3 RATIONAL AG CODES 55 2.4 EXERCISES 63 3 EXTENSIONS OF ALGEBRAIC FUNCTION FIELDS 67 3.1 ALGEBRAIC EXTENSIONS OF FUNCTION FIELDS 68 3.2 SUBRINGS OF FUNCTION FIELDS 77 3.3 LOCAL INTEGRAL BASES 81 3.4 THE COTRACE OF WEIL DIFFERENTIALS AND THE HURWITZ GENUS FORMULA 90 3.5 THE DIFFERENT 99 3.6 CONSTANT FIELD EXTENSIONS 112 3.7 GALOIS EXTENSIONS I 120 3.8 GALOIS EXTENSIONS II 130 3.9 RAMIFICATION AND SPLITTING IN THE COMPOSITUM OF FUNCTION FIELDS 137 3.10 INSEPARABLE EXTENSIONS 143 3.11 ESTIMATES FOR THE GENUS OF A FUNCTION FIELD 145 3.12 EXERCISES 150 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/990669424 DIGITALISIERT DURCH XII CONTENTS 4 DIFFERENTIALS OF ALGEBRAIC FUNCTION FIELDS 155 4.1 DERIVATIONS AND DIFFERENTIALS 155 4.2 THE P-ADIC COMPLETION 161 4.3 DIFFERENTIALS AND WEIL DIFFERENTIALS 170 4.4 EXERCISES 179 5 ALGEBRAIC FUNCTION FIELDS OVER FINITE CONSTANT FIELDS 185 5.1 THE ZETA FUNCTION OF A FUNCTION FIELD 185 5.2 THE HASSE-WEIL THEOREM 197 5.3 IMPROVEMENTS OF THE HASSE-WEIL BOUND 208 5.4 EXERCISES 212 6 EXAMPLES OF ALGEBRAIC FUNCTION FIELDS 217 6.1 ELLIPTIC FUNCTION FIELDS 217 6.2 HYPERELLIPTIC FUNCTION FIELDS 224 6.3 TARNE CYCLIC EXTENSIONS OF THE RATIONAL FUNCTION FIELD 227 6.4 SOME ELEMENTARY ABELIAN P-EXTENSIONS OF K(X), CHAXK = P 0 232 6.5 EXERCISES 235 7 ASYMPTOTIC BOUNDS FOR THE NUMBER OF RATIONAL PLACES .... 243 7.1 IHARA S CONSTANT A{Q) 243 7.2 TOWERS OF FUNCTION FIELDS 246 7.3 SOME TARNE TOWERS 259 7.4 SOME WILD TOWERS 261 7.5 EXERCISES 285 8 MORE ABOUT ALGEBRAIC GEOMETRY CODES 289 8.1 THE RESIDUE REPRESENTATION OF C N {D, G) 289 8.2 AUTOMORPHISMS OF AG CODES 290 8.3 HERMITIAN CODES 292 8.4 THE TSFASMAN-VLADUT-ZINK THEOREM 297 8. CONTENTS XIII REFERENCES 349 INDEX 353
any_adam_object	1
author2	Stichtenoth, Henning 1944-
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spelling	Algebraic function fields and codes Henning Stichtenoth second edition Berlin ; Heidelberg Springer 2009 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Graduate texts in mathematics 254 Algebraische Funktion (DE-588)4141836-0 gnd rswk-swf Fehlerkorrekturcode (DE-588)4124917-3 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Algebraischer Funktionenkörper (DE-588)4141850-5 gnd rswk-swf Algebraischer Funktionenkörper (DE-588)4141850-5 s Codierungstheorie (DE-588)4139405-7 s DE-604 Fehlerkorrekturcode (DE-588)4124917-3 s 1\p DE-604 Algebraische Funktion (DE-588)4141836-0 s 2\p DE-604 Stichtenoth, Henning 1944- (DE-588)141456280 edt Erscheint auch als Druck-Ausgabe Graduate texts in mathematics 254 (DE-604)BV035421258 254 https://doi.org/10.1007/978-3-540-76878-4 Verlag URL des Erstveröffentlichers Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017480634&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Algebraic function fields and codes Graduate texts in mathematics Algebraische Funktion (DE-588)4141836-0 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Codierungstheorie (DE-588)4139405-7 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd
subject_GND	(DE-588)4141836-0 (DE-588)4124917-3 (DE-588)4139405-7 (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	Algebraische Funktion (DE-588)4141836-0 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Codierungstheorie (DE-588)4139405-7 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd
topic_facet	Algebraische Funktion Fehlerkorrekturcode Codierungstheorie Algebraischer Funktionenkörper
url	https://doi.org/10.1007/978-3-540-76878-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017480634&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV035421258
work_keys_str_mv	AT stichtenothhenning algebraicfunctionfieldsandcodes

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