Algebraic function fields and codes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in mathematics
254 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 355 S. graph. Darst. |
| ISBN: | 9783540768777 9783642095566 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035240336 | ||
| 003 | DE-604 | ||
| 005 | 20130625 | ||
| 007 | t | ||
| 008 | 090112s2009 d||| |||| 00||| eng d | ||
| 020 | |a 9783540768777 |9 978-3-540-76877-7 | ||
| 020 | |a 9783642095566 |9 978-3-642-09556-6 | ||
| 035 | |a (OCoLC)277069402 | ||
| 035 | |a (DE-599)BVBBV035240336 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-824 |a DE-355 |a DE-703 |a DE-20 |a DE-188 |a DE-11 |a DE-91G |a DE-83 |a DE-706 | ||
| 050 | 0 | |a QA341 | |
| 082 | 0 | |a 512.74 |2 22 | |
| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 084 | |a MAT 140f |2 stub | ||
| 084 | |a MAT 125f |2 stub | ||
| 084 | |a 11R58 |2 msc | ||
| 084 | |a DAT 584f |2 stub | ||
| 100 | 1 | |a Stichtenoth, Henning |d 1944- |e Verfasser |0 (DE-588)141456280 |4 aut | |
| 245 | 1 | 0 | |a Algebraic function fields and codes |c Henning Stichtenoth |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XIII, 355 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 254 | |
| 650 | 4 | |a Algebraischer Funktionenkörper | |
| 650 | 4 | |a Algebraischer Funktionenkörper - Codierungstheorie | |
| 650 | 4 | |a Algebraic fields | |
| 650 | 4 | |a Algebraic functions | |
| 650 | 4 | |a Goppa codes | |
| 650 | 0 | 7 | |a Codierungstheorie |0 (DE-588)4139405-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fehlerkorrekturcode |0 (DE-588)4124917-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Funktion |0 (DE-588)4141836-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraischer Funktionenkörper |0 (DE-588)4141850-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraischer Funktionenkörper |0 (DE-588)4141850-5 |D s |
| 689 | 0 | 1 | |a Fehlerkorrekturcode |0 (DE-588)4124917-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Algebraische Funktion |0 (DE-588)4141836-0 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Algebraischer Funktionenkörper |0 (DE-588)4141850-5 |D s |
| 689 | 2 | 1 | |a Codierungstheorie |0 (DE-588)4139405-7 |D s |
| 689 | 2 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-540-76878-4 |
| 830 | 0 | |a Graduate texts in mathematics |v 254 |w (DE-604)BV000000067 |9 254 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017046140&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017046140 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804138512368271360 |
|---|---|
| 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
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 Tame Cyclic Extensions of the Rational Function Field 227
6.4 Some Elementary Abelian p-Extensions of K(x),
char K = 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 Tame 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 Cq(D, G) 289
8.2 Automorphisms of AG Codes 290
8.3 Hermitian Codes 292
8.4 The Tsfasman-Vladut-Zink Theorem 297
8.5 Decoding AG Codes 303
8.6 Exercises 308
9 Subfleld Subcodes and Trace Codes 311
9.1 On the Dimension of Subfield Subcodes and Trace Codes 311
9.2 Weights of Trace Codes 315
9.3 Exercises 325
Appendix A. Field Theory 327
Appendix B. Algebraic Curves and Function Fields 335
List of Notations 345
Contents XIII
References 349
Index 353
|
| any_adam_object | 1 |
| author | Stichtenoth, Henning 1944- |
| author_GND | (DE-588)141456280 |
| author_facet | Stichtenoth, Henning 1944- |
| author_role | aut |
| author_sort | Stichtenoth, Henning 1944- |
| author_variant | h s hs |
| building | Verbundindex |
| bvnumber | BV035240336 |
| callnumber-first | Q - Science |
| callnumber-label | QA341 |
| callnumber-raw | QA341 |
| callnumber-search | QA341 |
| callnumber-sort | QA 3341 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 |
| classification_tum | MAT 140f MAT 125f DAT 584f |
| ctrlnum | (OCoLC)277069402 (DE-599)BVBBV035240336 |
| 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 | 3512.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02526nam a2200625 cb4500</leader><controlfield tag="001">BV035240336</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130625 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">090112s2009 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783540768777</subfield><subfield code="9">978-3-540-76877-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642095566</subfield><subfield code="9">978-3-642-09556-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)277069402</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035240336</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA341</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.74</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 240</subfield><subfield code="0">(DE-625)143226:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 140f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 125f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">11R58</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">DAT 584f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Stichtenoth, Henning</subfield><subfield code="d">1944-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)141456280</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algebraic function fields and codes</subfield><subfield code="c">Henning Stichtenoth</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 355 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">254</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraischer Funktionenkörper</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraischer Funktionenkörper - Codierungstheorie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic fields</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Goppa codes</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Codierungstheorie</subfield><subfield code="0">(DE-588)4139405-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fehlerkorrekturcode</subfield><subfield code="0">(DE-588)4124917-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Funktion</subfield><subfield code="0">(DE-588)4141836-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraischer Funktionenkörper</subfield><subfield code="0">(DE-588)4141850-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraischer Funktionenkörper</subfield><subfield code="0">(DE-588)4141850-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Fehlerkorrekturcode</subfield><subfield code="0">(DE-588)4124917-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Algebraische Funktion</subfield><subfield code="0">(DE-588)4141836-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Algebraischer Funktionenkörper</subfield><subfield code="0">(DE-588)4141850-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Codierungstheorie</subfield><subfield code="0">(DE-588)4139405-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-540-76878-4</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">254</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">254</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017046140&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-017046140</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV035240336 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:29:22Z |
| institution | BVB |
| isbn | 9783540768777 9783642095566 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017046140 |
| oclc_num | 277069402 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-824 DE-355 DE-BY-UBR DE-703 DE-20 DE-188 DE-11 DE-91G DE-BY-TUM DE-83 DE-706 |
| owner_facet | DE-19 DE-BY-UBM DE-824 DE-355 DE-BY-UBR DE-703 DE-20 DE-188 DE-11 DE-91G DE-BY-TUM DE-83 DE-706 |
| physical | XIII, 355 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Stichtenoth, Henning 1944- Verfasser (DE-588)141456280 aut Algebraic function fields and codes Henning Stichtenoth 2. ed. Berlin [u.a.] Springer 2009 XIII, 355 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 254 Algebraischer Funktionenkörper Algebraischer Funktionenkörper - Codierungstheorie Algebraic fields Algebraic functions Goppa codes Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Fehlerkorrekturcode (DE-588)4124917-3 gnd rswk-swf Algebraische Funktion (DE-588)4141836-0 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 Erscheint auch als Online-Ausgabe 978-3-540-76878-4 Graduate texts in mathematics 254 (DE-604)BV000000067 254 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017046140&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 Graduate texts in mathematics Algebraischer Funktionenkörper Algebraischer Funktionenkörper - Codierungstheorie Algebraic fields Algebraic functions Goppa codes Codierungstheorie (DE-588)4139405-7 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Algebraische Funktion (DE-588)4141836-0 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd |
| subject_GND | (DE-588)4139405-7 (DE-588)4124917-3 (DE-588)4141836-0 (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 | Algebraischer Funktionenkörper Algebraischer Funktionenkörper - Codierungstheorie Algebraic fields Algebraic functions Goppa codes Codierungstheorie (DE-588)4139405-7 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Algebraische Funktion (DE-588)4141836-0 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd |
| topic_facet | Algebraischer Funktionenkörper Algebraischer Funktionenkörper - Codierungstheorie Algebraic fields Algebraic functions Goppa codes Codierungstheorie Fehlerkorrekturcode Algebraische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017046140&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT stichtenothhenning algebraicfunctionfieldsandcodes |