Codes on Algebraic Curves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1999
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A. |
| Beschreibung: | 1 Online-Ressource (XIII, 350 p) |
| ISBN: | 9781461547853 9781461371670 |
| DOI: | 10.1007/978-1-4615-4785-3 |
Internformat
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| 245 | 1 | 0 | |a Codes on Algebraic Curves |c by Serguei A. Stepanov |
| 264 | 1 | |a Boston, MA |b Springer US |c 1999 | |
| 300 | |a 1 Online-Ressource (XIII, 350 p) | ||
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| 500 | |a This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A. | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Geometry, algebraic | |
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Computer engineering | |
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| 650 | 0 | 7 | |a Goppa-Code |0 (DE-588)4218589-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Kurve |0 (DE-588)4001165-3 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Goppa-Code |0 (DE-588)4218589-0 |D s |
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Datensatz im Suchindex
| _version_ | 1804153093360713728 |
|---|---|
| any_adam_object | |
| author | Stepanov, Serguei A. |
| author_facet | Stepanov, Serguei A. |
| author_role | aut |
| author_sort | Stepanov, Serguei A. |
| author_variant | s a s sa sas |
| building | Verbundindex |
| bvnumber | BV042420893 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863678962 (DE-599)BVBBV042420893 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4615-4785-3 |
| format | Electronic eBook |
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| id | DE-604.BV042420893 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461547853 9781461371670 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856310 |
| oclc_num | 863678962 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XIII, 350 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer US |
| record_format | marc |
| spelling | Stepanov, Serguei A. Verfasser aut Codes on Algebraic Curves by Serguei A. Stepanov Boston, MA Springer US 1999 1 Online-Ressource (XIII, 350 p) txt rdacontent c rdamedia cr rdacarrier This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A. Mathematics Algebra Geometry, algebraic Algorithms Computer engineering Electrical Engineering Algebraic Geometry Mathematik Goppa-Code (DE-588)4218589-0 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 s Goppa-Code (DE-588)4218589-0 s 1\p DE-604 https://doi.org/10.1007/978-1-4615-4785-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stepanov, Serguei A. Codes on Algebraic Curves Mathematics Algebra Geometry, algebraic Algorithms Computer engineering Electrical Engineering Algebraic Geometry Mathematik Goppa-Code (DE-588)4218589-0 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| subject_GND | (DE-588)4218589-0 (DE-588)4001165-3 |
| title | Codes on Algebraic Curves |
| title_auth | Codes on Algebraic Curves |
| title_exact_search | Codes on Algebraic Curves |
| title_full | Codes on Algebraic Curves by Serguei A. Stepanov |
| title_fullStr | Codes on Algebraic Curves by Serguei A. Stepanov |
| title_full_unstemmed | Codes on Algebraic Curves by Serguei A. Stepanov |
| title_short | Codes on Algebraic Curves |
| title_sort | codes on algebraic curves |
| topic | Mathematics Algebra Geometry, algebraic Algorithms Computer engineering Electrical Engineering Algebraic Geometry Mathematik Goppa-Code (DE-588)4218589-0 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| topic_facet | Mathematics Algebra Geometry, algebraic Algorithms Computer engineering Electrical Engineering Algebraic Geometry Mathematik Goppa-Code Algebraische Kurve |
| url | https://doi.org/10.1007/978-1-4615-4785-3 |
| work_keys_str_mv | AT stepanovsergueia codesonalgebraiccurves |