Coding Theory and Number Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2003
|
| Schriftenreihe: | Mathematics and Its Applications
554,A |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book grew out of our lectures given in the Oberseminar on 'Coding Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001. The coding theory combines mathematical elegance and some engineering problems to an unusual degree. The major advantage of studying coding theory is the beauty of this particular combination of mathematics and engineering. In this book we wish to introduce some practical problems to the mathematician and to address these as an essential part of the development of modern number theory. The book consists of five chapters and an appendix. Chapter 1 may mostly be dropped from an introductory course of linear codes. In Chapter 2 we discuss some relations between the number of solutions of a diagonal equation over finite fields and the weight distribution of cyclic codes. Chapter 3 begins by reviewing some basic facts from elliptic curves over finite fields and modular forms, and shows that the weight distribution of the Melas codes is represented by means of the trace of the Hecke operators acting on the space of cusp forms. Chapter 4 is a systematic study of the algebraic-geometric codes. For a long time, the study of algebraic curves over finite fields was the province of pure mathematicians. In the period 1977 - 1982, V. D. Goppa discovered an amazing connection between the theory of algebraic curves over finite fields and the theory of q-ary codes |
| Beschreibung: | 1 Online-Ressource (XII, 148 p) |
| ISBN: | 9789401703055 9789048162574 |
| DOI: | 10.1007/978-94-017-0305-5 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042424197 | ||
| 003 | DE-604 | ||
| 005 | 20180110 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2003 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401703055 |c Online |9 978-94-017-0305-5 | ||
| 020 | |a 9789048162574 |c Print |9 978-90-481-6257-4 | ||
| 024 | 7 | |a 10.1007/978-94-017-0305-5 |2 doi | |
| 035 | |a (OCoLC)1184505375 | ||
| 035 | |a (DE-599)BVBBV042424197 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 004.0151 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Hiramatsu, Toyokazu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Coding Theory and Number Theory |c by Toyokazu Hiramatsu, Günter Köhler |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 2003 | |
| 300 | |a 1 Online-Ressource (XII, 148 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and Its Applications |v 554-A | |
| 500 | |a This book grew out of our lectures given in the Oberseminar on 'Coding Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001. The coding theory combines mathematical elegance and some engineering problems to an unusual degree. The major advantage of studying coding theory is the beauty of this particular combination of mathematics and engineering. In this book we wish to introduce some practical problems to the mathematician and to address these as an essential part of the development of modern number theory. The book consists of five chapters and an appendix. Chapter 1 may mostly be dropped from an introductory course of linear codes. In Chapter 2 we discuss some relations between the number of solutions of a diagonal equation over finite fields and the weight distribution of cyclic codes. Chapter 3 begins by reviewing some basic facts from elliptic curves over finite fields and modular forms, and shows that the weight distribution of the Melas codes is represented by means of the trace of the Hecke operators acting on the space of cusp forms. Chapter 4 is a systematic study of the algebraic-geometric codes. For a long time, the study of algebraic curves over finite fields was the province of pure mathematicians. In the period 1977 - 1982, V. D. Goppa discovered an amazing connection between the theory of algebraic curves over finite fields and the theory of q-ary codes | ||
| 650 | 4 | |a Computer science | |
| 650 | 4 | |a Coding theory | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Geometry, algebraic | |
| 650 | 4 | |a Matrix theory | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Computer Science | |
| 650 | 4 | |a Discrete Mathematics in Computer Science | |
| 650 | 4 | |a Algebraic Geometry | |
| 650 | 4 | |a Number Theory | |
| 650 | 4 | |a Coding and Information Theory | |
| 650 | 4 | |a Linear and Multilinear Algebras, Matrix Theory | |
| 650 | 4 | |a Informatik | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Codierungstheorie |0 (DE-588)4139405-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Codierungstheorie |0 (DE-588)4139405-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 700 | 1 | |a Köhler, Günter |e Sonstige |4 oth | |
| 830 | 0 | |a Mathematics and Its Applications |v 554,A |w (DE-604)BV008163334 |9 554,A | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-017-0305-5 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859614 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153100867469312 |
|---|---|
| any_adam_object | |
| author | Hiramatsu, Toyokazu |
| author_facet | Hiramatsu, Toyokazu |
| author_role | aut |
| author_sort | Hiramatsu, Toyokazu |
| author_variant | t h th |
| building | Verbundindex |
| bvnumber | BV042424197 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184505375 (DE-599)BVBBV042424197 |
| dewey-full | 004.0151 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 004 - Computer science |
| dewey-raw | 004.0151 |
| dewey-search | 004.0151 |
| dewey-sort | 14.0151 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| doi_str_mv | 10.1007/978-94-017-0305-5 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03718nmm a2200637zcb4500</leader><controlfield tag="001">BV042424197</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180110 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2003 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401703055</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-017-0305-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048162574</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-6257-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-017-0305-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1184505375</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424197</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">004.0151</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hiramatsu, Toyokazu</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Coding Theory and Number Theory</subfield><subfield code="c">by Toyokazu Hiramatsu, Günter Köhler</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 148 p)</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">554-A</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book grew out of our lectures given in the Oberseminar on 'Coding Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001. The coding theory combines mathematical elegance and some engineering problems to an unusual degree. The major advantage of studying coding theory is the beauty of this particular combination of mathematics and engineering. In this book we wish to introduce some practical problems to the mathematician and to address these as an essential part of the development of modern number theory. The book consists of five chapters and an appendix. Chapter 1 may mostly be dropped from an introductory course of linear codes. In Chapter 2 we discuss some relations between the number of solutions of a diagonal equation over finite fields and the weight distribution of cyclic codes. Chapter 3 begins by reviewing some basic facts from elliptic curves over finite fields and modular forms, and shows that the weight distribution of the Melas codes is represented by means of the trace of the Hecke operators acting on the space of cusp forms. Chapter 4 is a systematic study of the algebraic-geometric codes. For a long time, the study of algebraic curves over finite fields was the province of pure mathematicians. In the period 1977 - 1982, V. D. Goppa discovered an amazing connection between the theory of algebraic curves over finite fields and the theory of q-ary codes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Coding theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computational complexity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, algebraic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrix theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer Science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discrete Mathematics in Computer Science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Coding and Information Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear and Multilinear Algebras, Matrix Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Informatik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</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="689" ind1="0" ind2="0"><subfield code="a">Codierungstheorie</subfield><subfield code="0">(DE-588)4139405-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Köhler, Günter</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">554,A</subfield><subfield code="w">(DE-604)BV008163334</subfield><subfield code="9">554,A</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-017-0305-5</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859614</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><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\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.BV042424197 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401703055 9789048162574 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859614 |
| oclc_num | 1184505375 |
| 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 (XII, 148 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer Netherlands |
| record_format | marc |
| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Hiramatsu, Toyokazu Verfasser aut Coding Theory and Number Theory by Toyokazu Hiramatsu, Günter Köhler Dordrecht Springer Netherlands 2003 1 Online-Ressource (XII, 148 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 554-A This book grew out of our lectures given in the Oberseminar on 'Coding Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001. The coding theory combines mathematical elegance and some engineering problems to an unusual degree. The major advantage of studying coding theory is the beauty of this particular combination of mathematics and engineering. In this book we wish to introduce some practical problems to the mathematician and to address these as an essential part of the development of modern number theory. The book consists of five chapters and an appendix. Chapter 1 may mostly be dropped from an introductory course of linear codes. In Chapter 2 we discuss some relations between the number of solutions of a diagonal equation over finite fields and the weight distribution of cyclic codes. Chapter 3 begins by reviewing some basic facts from elliptic curves over finite fields and modular forms, and shows that the weight distribution of the Melas codes is represented by means of the trace of the Hecke operators acting on the space of cusp forms. Chapter 4 is a systematic study of the algebraic-geometric codes. For a long time, the study of algebraic curves over finite fields was the province of pure mathematicians. In the period 1977 - 1982, V. D. Goppa discovered an amazing connection between the theory of algebraic curves over finite fields and the theory of q-ary codes Computer science Coding theory Computational complexity Geometry, algebraic Matrix theory Number theory Computer Science Discrete Mathematics in Computer Science Algebraic Geometry Number Theory Coding and Information Theory Linear and Multilinear Algebras, Matrix Theory Informatik Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 s 1\p DE-604 Zahlentheorie (DE-588)4067277-3 s 2\p DE-604 Köhler, Günter Sonstige oth Mathematics and Its Applications 554,A (DE-604)BV008163334 554,A https://doi.org/10.1007/978-94-017-0305-5 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 | Hiramatsu, Toyokazu Coding Theory and Number Theory Mathematics and Its Applications Computer science Coding theory Computational complexity Geometry, algebraic Matrix theory Number theory Computer Science Discrete Mathematics in Computer Science Algebraic Geometry Number Theory Coding and Information Theory Linear and Multilinear Algebras, Matrix Theory Informatik Zahlentheorie (DE-588)4067277-3 gnd Codierungstheorie (DE-588)4139405-7 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4139405-7 |
| title | Coding Theory and Number Theory |
| title_auth | Coding Theory and Number Theory |
| title_exact_search | Coding Theory and Number Theory |
| title_full | Coding Theory and Number Theory by Toyokazu Hiramatsu, Günter Köhler |
| title_fullStr | Coding Theory and Number Theory by Toyokazu Hiramatsu, Günter Köhler |
| title_full_unstemmed | Coding Theory and Number Theory by Toyokazu Hiramatsu, Günter Köhler |
| title_short | Coding Theory and Number Theory |
| title_sort | coding theory and number theory |
| topic | Computer science Coding theory Computational complexity Geometry, algebraic Matrix theory Number theory Computer Science Discrete Mathematics in Computer Science Algebraic Geometry Number Theory Coding and Information Theory Linear and Multilinear Algebras, Matrix Theory Informatik Zahlentheorie (DE-588)4067277-3 gnd Codierungstheorie (DE-588)4139405-7 gnd |
| topic_facet | Computer science Coding theory Computational complexity Geometry, algebraic Matrix theory Number theory Computer Science Discrete Mathematics in Computer Science Algebraic Geometry Number Theory Coding and Information Theory Linear and Multilinear Algebras, Matrix Theory Informatik Zahlentheorie Codierungstheorie |
| url | https://doi.org/10.1007/978-94-017-0305-5 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT hiramatsutoyokazu codingtheoryandnumbertheory AT kohlergunter codingtheoryandnumbertheory |