Lattices, modular forms, and local weight enumerators of ternary self-dual codes:
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| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2000
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 87 S. |
Internformat
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Datensatz im Suchindex
| _version_ | 1807504586473209856 |
|---|---|
| adam_text |
CONTENTS
PREFACE
2
1
INTRODUCTION
TO
LINEAR
CODES
AND
MODULAR
FORMS
S
1.1
LINEAR
CODES
.
5
1.2
MODULAR
FORMS
.
9
2
TERNARY
SELF-DUAL
CODES
13
2.1
INTRODUCTION
.
13
2.2
DESIGNS
.
15
2.3
CODEWORDS
OF
WEIGHT
3
.
16
2.4
CLASSIFICATION
OF
TERNARY
SELF-DUAL
CODES
OF
LENGTH
16,20,
AND
24
20
3
LATTICES
24
3.1
INTRODUCTION
.
24
3.2
THE
ROOT
LATTICE
A
N
.
30
3.3
THE
THETA-FUNCTIONS
OF
A
2
AND
A
2
.
33
3.4
THE
LATTICE
OF
A
TERNARY
SELF-DUAL
CODE
.
36
3.5
THE
LATTICE
OF
C
G
{A
2
/A
2
)
2
.
39
4
SPHERICAL
THETA-FUNCTIONS
41
4.1
SPHERICAL
POLYNOMIALS
.
41
CONTENTS
1
4.2
THE
SPHERICAL
THETA-FUNCTION
OF
A
TERNARY
SELF-DUAL
CODE
I
.
.
.
45
4.3
THE
FUNCTION
9
C
.
46
4.4
THE
SPHERICAL
THETA
FUNCTION
OF
A
TERNARY
SELF-DUAL
CODE
II
.
.
52
5
LOCAL
WEIGHT
ENUMERATORS
58
5.1
INTRODUCTION
.
58
5.2
NECESSARY
CRITERIA
FOR
=
0
.
60
5.3
THE
LOCAL
WEIGHT-ENUMERATOR
AND
THE
SPHERICAL
THETA-FUNCTION
.
61
6
A
GLEASON-TYPE
THEOREM
63
6.1
SUFFICIENT
CRITERIA
FOR
W
U1I)
=
0
.
63
6.2
THEOREM
AND
PROOF
.
65
6.3
A
MACWILLIAMS-TYPE
THEOREM
.
69
6.4
EXAMPLES
.
71
7
APPLICATIONS
73
7.1
EXTREMAL
CODES
.
73
7.2
SYMMETRY
CODES
.
74
7.3
TERNARY
SELF-DUAL
CODES
OF
LENGTH
16
.
76
8
OUTLOOK
80
8.1
GENERALIZATION
OF
THE
LOCAL
MINIMUM
WEIGHT
.
80
8.2
EXAMPLES
.
82 |
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| bvnumber | BV013383560 |
| classification_tum | DAT 580d |
| ctrlnum | (OCoLC)48742541 (DE-599)BVBBV013383560 |
| discipline | Informatik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV013383560 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-16T01:11:39Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009129097 |
| oclc_num | 48742541 |
| open_access_boolean | |
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| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-12 DE-824 DE-83 DE-188 |
| physical | 87 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| record_format | marc |
| spelling | Kunitz, Katja 1970- Verfasser (DE-588)122270967 aut Lattices, modular forms, and local weight enumerators of ternary self-dual codes Katja Kunitz 2000 87 S. txt rdacontent n rdamedia nc rdacarrier Braunschweig, Techn. Univ., Diss., 2000 Codierungstheorie gtt Hochschulschrift gtt Gitter Mathematik (DE-588)4157375-4 gnd rswk-swf Linearer Code (DE-588)4524827-8 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Thetafunktion (DE-588)4185175-4 gnd rswk-swf Modulare Darstellung (DE-588)4311996-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Codierungstheorie (DE-588)4139405-7 s Gitter Mathematik (DE-588)4157375-4 s DE-604 Modulare Darstellung (DE-588)4311996-7 s Linearer Code (DE-588)4524827-8 s Thetafunktion (DE-588)4185175-4 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009129097&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kunitz, Katja 1970- Lattices, modular forms, and local weight enumerators of ternary self-dual codes Codierungstheorie gtt Hochschulschrift gtt Gitter Mathematik (DE-588)4157375-4 gnd Linearer Code (DE-588)4524827-8 gnd Codierungstheorie (DE-588)4139405-7 gnd Thetafunktion (DE-588)4185175-4 gnd Modulare Darstellung (DE-588)4311996-7 gnd |
| subject_GND | (DE-588)4157375-4 (DE-588)4524827-8 (DE-588)4139405-7 (DE-588)4185175-4 (DE-588)4311996-7 (DE-588)4113937-9 |
| title | Lattices, modular forms, and local weight enumerators of ternary self-dual codes |
| title_auth | Lattices, modular forms, and local weight enumerators of ternary self-dual codes |
| title_exact_search | Lattices, modular forms, and local weight enumerators of ternary self-dual codes |
| title_full | Lattices, modular forms, and local weight enumerators of ternary self-dual codes Katja Kunitz |
| title_fullStr | Lattices, modular forms, and local weight enumerators of ternary self-dual codes Katja Kunitz |
| title_full_unstemmed | Lattices, modular forms, and local weight enumerators of ternary self-dual codes Katja Kunitz |
| title_short | Lattices, modular forms, and local weight enumerators of ternary self-dual codes |
| title_sort | lattices modular forms and local weight enumerators of ternary self dual codes |
| topic | Codierungstheorie gtt Hochschulschrift gtt Gitter Mathematik (DE-588)4157375-4 gnd Linearer Code (DE-588)4524827-8 gnd Codierungstheorie (DE-588)4139405-7 gnd Thetafunktion (DE-588)4185175-4 gnd Modulare Darstellung (DE-588)4311996-7 gnd |
| topic_facet | Codierungstheorie Hochschulschrift Gitter Mathematik Linearer Code Thetafunktion Modulare Darstellung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009129097&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kunitzkatja latticesmodularformsandlocalweightenumeratorsofternaryselfdualcodes |