Geometry and codes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1988
|
| Schriftenreihe: | [Mathematics and its applications / Soviet series]
24 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | IX, 157 S. |
| ISBN: | 9027727767 |
Internformat
MARC
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| 100 | 1 | |a Goppa, V. D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometry and codes |c V. D. Goppa |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1988 | |
| 300 | |a IX, 157 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a [Mathematics and its applications / Soviet series] |v 24 | |
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| 650 | 7 | |a Algebraïsche meetkunde |2 gtt | |
| 650 | 7 | |a Coderingstheorie |2 gtt | |
| 650 | 4 | |a Codes correcteurs d'erreurs (Théorie de l'information) | |
| 650 | 7 | |a Codes correcteurs d'erreurs (théorie de l'information) |2 ram | |
| 650 | 4 | |a Géométrie | |
| 650 | 7 | |a approximation rationnelle |2 inriac | |
| 650 | 7 | |a code correcteur erreur |2 inriac | |
| 650 | 7 | |a code jacobien |2 inriac | |
| 650 | 7 | |a courbe algébrique |2 inriac | |
| 650 | 7 | |a décodage |2 inriac | |
| 650 | 7 | |a géométrie algébrique |2 inriac | |
| 650 | 7 | |a géométrie algébrique |2 ram | |
| 650 | 7 | |a théorie codage |2 inriac | |
| 650 | 7 | |a théorie information |2 inriac | |
| 650 | 7 | |a théorème Riemann-Roch |2 inriac | |
| 650 | 4 | |a Error-correcting codes (Information theory) | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 0 | 7 | |a Geometrie |0 (DE-588)4020236-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fehlerkorrekturcode |0 (DE-588)4124917-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804117944098095104 |
|---|---|
| adam_text | Table of Contents
Chapter 1. Rational Codes 1
1 Notion of Error Correcting Code 1
2 Linear Codes 2
3 Decoding 6
4 Extension of the Ground Field 7
5 Hamming Code Correcting a Single Error 9
6 Ovals in the Projective Plane 10
7 Codes on a Twisted Cubic Curve 18
8 Normal Rational Codes 23
9 Rational Functions 27
10 Differential Representation of Codes 33
11 Code Projections 37
12 Linear Hashing 43
Chapter 2. Decoding and Rational Approximations 47
1 Continued Fractions 47
2 The Fermat Theorem on the Sum of Two Squares 49
3 Approximations in the/ adic Metric 50
4 Decoding Algorithm 52
5 Linear Recurrent Sequences and Shift Registers 54
6 Linear Discrete Filters 62
7 Functions with Rational Spectrum 68
8 Rational Interpolation 70
9 Numerical Encoding 72
Chapter 3. Algebraic Curves 78
1 Affine and Projective Curves 78
viii Table of Contents
2 Intersection of Curves. Bezout Theorem 79
3 Singular Points of a Curve 81
4 Linear Systems of Curves 83
5 Fundamental Noether Theorem 85
6 Rational Functions and Divisors 88
7 Riemann Roch Problem 91
8 Riemann Roch Theorem 95
9 Quadratic Transformations 98
10 Projective Model of the Linear System 102
11 Differentials on a Curve 105
12 Zeta Function of a Curve 110
Chapter 4. Generalized Jacobian Codes 115
1 The ^equivalence on Curves. Definition of the Code 115
2 Local Symbol. Error Correcting Capacity of a Code 117
3 The Structure of the Error Checking Matrix 119
4 Elliptic Curves 120
5 Jacobian of a Curve 124
6 The Generalized Jacobian Variety 127
7 The Fermat and Hermite Curves 129
8 Modular Curves 131
9 Codes Based on Rational Mapping 135
10 Covering Curves 149
11 Geometric Decoding 153
References 155
Index 157
|
| any_adam_object | 1 |
| author | Goppa, V. D. |
| author_facet | Goppa, V. D. |
| author_role | aut |
| author_sort | Goppa, V. D. |
| author_variant | v d g vd vdg |
| building | Verbundindex |
| bvnumber | BV003593959 |
| callnumber-first | Q - Science |
| callnumber-label | QA268 |
| callnumber-raw | QA268 |
| callnumber-search | QA268 |
| callnumber-sort | QA 3268 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 170 SK 240 |
| ctrlnum | (OCoLC)18049752 (DE-599)BVBBV003593959 |
| dewey-full | 005.7/2 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.7/2 |
| dewey-search | 005.7/2 |
| dewey-sort | 15.7 12 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV003593959 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:02:27Z |
| institution | BVB |
| isbn | 9027727767 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002288442 |
| oclc_num | 18049752 |
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| physical | IX, 157 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Kluwer |
| record_format | marc |
| series2 | [Mathematics and its applications / Soviet series] |
| spelling | Goppa, V. D. Verfasser aut Geometry and codes V. D. Goppa Dordrecht [u.a.] Kluwer 1988 IX, 157 S. txt rdacontent n rdamedia nc rdacarrier [Mathematics and its applications / Soviet series] 24 Aus dem Russ. übers. Algebraïsche meetkunde gtt Coderingstheorie gtt Codes correcteurs d'erreurs (Théorie de l'information) Codes correcteurs d'erreurs (théorie de l'information) ram Géométrie approximation rationnelle inriac code correcteur erreur inriac code jacobien inriac courbe algébrique inriac décodage inriac géométrie algébrique inriac géométrie algébrique ram théorie codage inriac théorie information inriac théorème Riemann-Roch inriac Error-correcting codes (Information theory) Geometry, Algebraic Geometrie (DE-588)4020236-7 gnd rswk-swf Fehlerkorrekturcode (DE-588)4124917-3 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Geometrie (DE-588)4020236-7 s Fehlerkorrekturcode (DE-588)4124917-3 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s Codierungstheorie (DE-588)4139405-7 s Soviet series] [Mathematics and its applications 24 (DE-604)BV004708148 24 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002288442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goppa, V. D. Geometry and codes Algebraïsche meetkunde gtt Coderingstheorie gtt Codes correcteurs d'erreurs (Théorie de l'information) Codes correcteurs d'erreurs (théorie de l'information) ram Géométrie approximation rationnelle inriac code correcteur erreur inriac code jacobien inriac courbe algébrique inriac décodage inriac géométrie algébrique inriac géométrie algébrique ram théorie codage inriac théorie information inriac théorème Riemann-Roch inriac Error-correcting codes (Information theory) Geometry, Algebraic Geometrie (DE-588)4020236-7 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Codierungstheorie (DE-588)4139405-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4124917-3 (DE-588)4139405-7 (DE-588)4001161-6 |
| title | Geometry and codes |
| title_auth | Geometry and codes |
| title_exact_search | Geometry and codes |
| title_full | Geometry and codes V. D. Goppa |
| title_fullStr | Geometry and codes V. D. Goppa |
| title_full_unstemmed | Geometry and codes V. D. Goppa |
| title_short | Geometry and codes |
| title_sort | geometry and codes |
| topic | Algebraïsche meetkunde gtt Coderingstheorie gtt Codes correcteurs d'erreurs (Théorie de l'information) Codes correcteurs d'erreurs (théorie de l'information) ram Géométrie approximation rationnelle inriac code correcteur erreur inriac code jacobien inriac courbe algébrique inriac décodage inriac géométrie algébrique inriac géométrie algébrique ram théorie codage inriac théorie information inriac théorème Riemann-Roch inriac Error-correcting codes (Information theory) Geometry, Algebraic Geometrie (DE-588)4020236-7 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Codierungstheorie (DE-588)4139405-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algebraïsche meetkunde Coderingstheorie Codes correcteurs d'erreurs (Théorie de l'information) Codes correcteurs d'erreurs (théorie de l'information) Géométrie approximation rationnelle code correcteur erreur code jacobien courbe algébrique décodage géométrie algébrique théorie codage théorie information théorème Riemann-Roch Error-correcting codes (Information theory) Geometry, Algebraic Geometrie Fehlerkorrekturcode Codierungstheorie Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002288442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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