Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
1994
|
| Schriftenreihe: | Advanced Lectures in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. This book is about an example of such a connection: the relation between codes and lattices. Lattices are studied in number theory and in the geometry of numbers. Many problems about codes have their counterpart in problems about lattices and sphere packings. We give a detailed introduction to these relations including recent results of G. van der Geer and F. Hirzebruch. Let us explain the history of this book. In [LPS82] J. S. Leon, V. Pless, and N. J. A. Sloane considered the Lee weight enumerators of self-dual codes over the prime field of characteristic 5. They wrote in the introduction to their paper: "The weight enumerator of anyone of the codes . . . is strongly constrained: it must be invariant under a three-dimensional representation of the icosahedral group. These invariants were already known to Felix Klein, and the consequences for coding theory were discovered by Gleason and Pierce (and independently by the third author) . . . (It is worth mentioning that precisely the same invariants have recently been studied by Hirzebruch in connection with cusps of the Hilbert modular surface associated with Q( J5) |
| Beschreibung: | 1 Online-Ressource (XVI, 178 p) |
| ISBN: | 9783322968791 9783528064976 |
| ISSN: | 0932-7134 |
| DOI: | 10.1007/978-3-322-96879-1 |
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Datensatz im Suchindex
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| adam_text | |
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| author | Ebeling, Wolfgang 1951-2025 |
| author_GND | (DE-588)141552123 |
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| author_sort | Ebeling, Wolfgang 1951-2025 |
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| building | Verbundindex |
| bvnumber | BV042422384 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-full | 620 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620 |
| dewey-search | 620 |
| dewey-sort | 3620 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-322-96879-1 |
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| id | DE-604.BV042422384 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-15T07:00:32Z |
| institution | BVB |
| isbn | 9783322968791 9783528064976 |
| issn | 0932-7134 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857801 |
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| series2 | Advanced Lectures in Mathematics |
| spelling | Ebeling, Wolfgang 1951-2025 Verfasser (DE-588)141552123 aut Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch by Wolfgang Ebeling Wiesbaden Vieweg+Teubner Verlag 1994 1 Online-Ressource (XVI, 178 p) txt rdacontent c rdamedia cr rdacarrier Advanced Lectures in Mathematics 0932-7134 The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. This book is about an example of such a connection: the relation between codes and lattices. Lattices are studied in number theory and in the geometry of numbers. Many problems about codes have their counterpart in problems about lattices and sphere packings. We give a detailed introduction to these relations including recent results of G. van der Geer and F. Hirzebruch. Let us explain the history of this book. In [LPS82] J. S. Leon, V. Pless, and N. J. A. Sloane considered the Lee weight enumerators of self-dual codes over the prime field of characteristic 5. They wrote in the introduction to their paper: "The weight enumerator of anyone of the codes . . . is strongly constrained: it must be invariant under a three-dimensional representation of the icosahedral group. These invariants were already known to Felix Klein, and the consequences for coding theory were discovered by Gleason and Pierce (and independently by the third author) . . . (It is worth mentioning that precisely the same invariants have recently been studied by Hirzebruch in connection with cusps of the Hilbert modular surface associated with Q( J5) Engineering Engineering, general Ingenieurwissenschaften Code (DE-588)4010345-6 gnd rswk-swf Gitter Mathematik (DE-588)4157375-4 gnd rswk-swf Verband Mathematik (DE-588)4062565-5 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 s Gitter Mathematik (DE-588)4157375-4 s 1\p DE-604 Verband Mathematik (DE-588)4062565-5 s Code (DE-588)4010345-6 s 2\p DE-604 https://doi.org/10.1007/978-3-322-96879-1 Verlag Volltext 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 | Ebeling, Wolfgang 1951-2025 Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch Engineering Engineering, general Ingenieurwissenschaften Code (DE-588)4010345-6 gnd Gitter Mathematik (DE-588)4157375-4 gnd Verband Mathematik (DE-588)4062565-5 gnd Codierungstheorie (DE-588)4139405-7 gnd |
| subject_GND | (DE-588)4010345-6 (DE-588)4157375-4 (DE-588)4062565-5 (DE-588)4139405-7 |
| title | Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch |
| title_auth | Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch |
| title_exact_search | Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch |
| title_full | Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch by Wolfgang Ebeling |
| title_fullStr | Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch by Wolfgang Ebeling |
| title_full_unstemmed | Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch by Wolfgang Ebeling |
| title_short | Lattices and Codes |
| title_sort | lattices and codes a course partially based on lectures by f hirzebruch |
| title_sub | A Course Partially Based on Lectures by F. Hirzebruch |
| topic | Engineering Engineering, general Ingenieurwissenschaften Code (DE-588)4010345-6 gnd Gitter Mathematik (DE-588)4157375-4 gnd Verband Mathematik (DE-588)4062565-5 gnd Codierungstheorie (DE-588)4139405-7 gnd |
| topic_facet | Engineering Engineering, general Ingenieurwissenschaften Code Gitter Mathematik Verband Mathematik Codierungstheorie |
| url | https://doi.org/10.1007/978-3-322-96879-1 |
| work_keys_str_mv | AT ebelingwolfgang latticesandcodesacoursepartiallybasedonlecturesbyfhirzebruch |