Rational points on curves over finite fields: theory and applications
Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves ove...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2001
|
| Schriftenreihe: | London Mathematical Society lecture note series
285 |
| Links: | https://doi.org/10.1017/CBO9781107325951 |
| Zusammenfassung: | Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences. |
| Umfang: | 1 Online-Ressource (x, 245 Seiten) |
| ISBN: | 9781107325951 |
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| 520 | |a Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences. | ||
| 700 | 1 | |a Xing, Chaoping |d 1963- | |
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| spelling | Niederreiter, Harald 1944- Rational points on curves over finite fields theory and applications Harald Niederreiter, Chaoping Xing Cambridge Cambridge University Press 2001 1 Online-Ressource (x, 245 Seiten) txt c cr London Mathematical Society lecture note series 285 Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences. Xing, Chaoping 1963- Erscheint auch als Druck-Ausgabe 9780521665438 |
| spellingShingle | Niederreiter, Harald 1944- Rational points on curves over finite fields theory and applications |
| title | Rational points on curves over finite fields theory and applications |
| title_auth | Rational points on curves over finite fields theory and applications |
| title_exact_search | Rational points on curves over finite fields theory and applications |
| title_full | Rational points on curves over finite fields theory and applications Harald Niederreiter, Chaoping Xing |
| title_fullStr | Rational points on curves over finite fields theory and applications Harald Niederreiter, Chaoping Xing |
| title_full_unstemmed | Rational points on curves over finite fields theory and applications Harald Niederreiter, Chaoping Xing |
| title_short | Rational points on curves over finite fields |
| title_sort | rational points on curves over finite fields theory and applications |
| title_sub | theory and applications |
| work_keys_str_mv | AT niederreiterharald rationalpointsoncurvesoverfinitefieldstheoryandapplications AT xingchaoping rationalpointsoncurvesoverfinitefieldstheoryandapplications |