The theory of rectangular codes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Düsseldorf
VDI-Verl.
1999
|
| Schriftenreihe: | Verein Deutscher Ingenieure: [Fortschrittberichte VDI / 10]
Nur. 610 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 102 Seiten Diagramme |
| ISBN: | 3183610108 |
Internformat
MARC
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| 100 | 1 | |a Maucher, Johannes |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The theory of rectangular codes |c Johannes Maucher |
| 264 | 1 | |a Düsseldorf |b VDI-Verl. |c 1999 | |
| 300 | |a VI, 102 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Verein Deutscher Ingenieure: [Fortschrittberichte VDI / 10] |v Nur. 610 | |
| 502 | |b Dissertation |c Universität Ulm |d 1999 | ||
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Datensatz im Suchindex
| _version_ | 1807772961556398080 |
|---|---|
| adam_text |
V
CONTENTS
1
INTRODUCTION
1
2
THE
MINIMAL
TRELLIS
OF
BLOCK
CODES
5
2.1
DEFINITION
OF
TRELLISES
.
6
2.2
TRELLIS
REPRESENTATIONS
OF
BLOCK
CODES
.
7
2.3
RECTANGULAR
CODES
.
10
3
RECTANGULAR
CLOSURE
AND
BASIS
15
3.1
UNIVERSAL
ALGEBRA
.
16
3.2
ELEMENTS
AND
OPERATIONS
IN
RECT.
ALGEBRA
.
18
3.3
THE
RECTANGULAR
CLOSURE
.
21
3.3.1
THE
TAILSET
ALGORITHM
.
23
3.3.2
THE
MERGING
ALGORITHM
.
23
3.4
THE
RECTANGULAR
BASIS
OF
A
CODE
.
26
4
THE
BASIS
CARDINALITY
30
4.1
RECTANGULAR
CODES
OF
LENGTH
N
=
2
.
31
4.1.1
LENGTH
2
INTERPRETATION
OF
A
LENGTH
N
CODE
.
32
4.1.2
CONNECTIONS
IN
THE
CARTESIAN
ARRAYS
.
33
4.1.3
INDUCED
VECTORS
IN
THE
CLOSURE
R(X)
.
36
4.1.4
THE
CARDINALITY
OF
A
RECTANGULAR
BASIS
.
39
4.1.5
THE
BASIS
EXCHANGE
PROPERTY
.
41
4.2
RECTANGULAR
CODES
OF
ARBITRARY
LENGTH
N
.
43
4.2.1
RECTANGULAR
CLOSURE
OPERATION
IN
THE
CARTESIAN
ARRAY
.
45
4.2.2
QUASI
CONNECTED
CHAINS
OF
INDUCED
WORDS
.
47
4.2.3
CLASSIFICATION
OF
RECTANGULAR
ALGEBRA
.
50
VI
CONTENTS
5
BOUNDS
ON
BASIS
AND
TRELLIS
SIZE
52
5.1
QUASI
CONNECTED
CHAINS
AND
LINEAR
COMBINATIONS
.
53
5.1.1
ADDITION
OF
BINARY
VECTORS
WITHIN
A
QUASI
CONNECTED
CHAIN
53
5.1.2
TTI-ADDITION
OF
VECTORS
WITHIN
A
QUASI
CONNECTED
CHAIN
.
.
55
5.1.3
RECTANGULAR
AND
LINEAR
DEPENDENCE
.
58
5.2
LOWER
BOUNDS
FOR
THE
BASIS
CARDINALITY
.
58
5.3
UPPER
BOUND
ON
THE
TRELLIS
COMPLEXITY
.
59
6
CLASSES
OF
RECTANGULAR
CODES
62
6.1
RECTANGULAR
BASIS
OF
A
LINEAR
CODE
.
62
6.1.1
CONSTRUCTION
OF
THE
MINIMAL
TRELLIS
FROM
THE
TRELLIS
ORI
ENTED
GENERATOR
MATRIX
.
63
6.1.2
CONSTRUCTION
OF
A
RECTANGULAR
BASIS
FROM
THE
TRELLIS
ORI
ENTED
GENERATOR
MATRIX
.
66
6.2
COMBINATIONS
OF
RECTANGULAR
CODES
.
71
6.3
RECTANGULARITY
OF
WELL
KNOWN
NONLINEAR
CODES
.
72
6.4
RECTANGULAR
PRIME
CODES
.
73
6.4.1
RECTANGULAR
PRIME
LINEAR
CODES
.
75
6.4.2
THE
MINIMAL
SPAN
LENGTH
OF
LINEAR
CYCLIC
CODES
.
76
6.5
PERMUTATIONS
OF
RECTANGULAR
CODES
.
77
7
RECT.
CODES
IN
DECODING
ALGORITHMS
80
7.1
THE
SET
OF
MINIMUM
WEIGHT
CODEWORDS
.
81
7.2
DECODING
IN
THE
TRELLIS
OF
THE
CLOSURE
RFCIYY,)
.
84
8
CONCLUSION
86
A
PROOF
OF
COLORING
ALGORITHM
89 |
| any_adam_object | 1 |
| author | Maucher, Johannes |
| author_facet | Maucher, Johannes |
| author_role | aut |
| author_sort | Maucher, Johannes |
| author_variant | j m jm |
| building | Verbundindex |
| bvnumber | BV012942272 |
| classification_rvk | SK 170 |
| classification_tum | DAT 580d |
| ctrlnum | (OCoLC)45454684 (DE-599)BVBBV012942272 |
| discipline | Informatik Mathematik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV012942272 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-19T00:17:23Z |
| institution | BVB |
| isbn | 3183610108 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008811818 |
| oclc_num | 45454684 |
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| owner_facet | DE-91 DE-BY-TUM DE-210 DE-83 DE-29T |
| physical | VI, 102 Seiten Diagramme |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | VDI-Verl. |
| record_format | marc |
| series2 | Verein Deutscher Ingenieure: [Fortschrittberichte VDI / 10] |
| spelling | Maucher, Johannes Verfasser aut The theory of rectangular codes Johannes Maucher Düsseldorf VDI-Verl. 1999 VI, 102 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Verein Deutscher Ingenieure: [Fortschrittberichte VDI / 10] Nur. 610 Dissertation Universität Ulm 1999 Rechteckcode (DE-588)4583995-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Rechteckcode (DE-588)4583995-5 s DE-604 10] Verein Deutscher Ingenieure: [Fortschrittberichte VDI Nur. 610 (DE-604)BV000897204 610 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008811818&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Maucher, Johannes The theory of rectangular codes Rechteckcode (DE-588)4583995-5 gnd |
| subject_GND | (DE-588)4583995-5 (DE-588)4113937-9 |
| title | The theory of rectangular codes |
| title_auth | The theory of rectangular codes |
| title_exact_search | The theory of rectangular codes |
| title_full | The theory of rectangular codes Johannes Maucher |
| title_fullStr | The theory of rectangular codes Johannes Maucher |
| title_full_unstemmed | The theory of rectangular codes Johannes Maucher |
| title_short | The theory of rectangular codes |
| title_sort | the theory of rectangular codes |
| topic | Rechteckcode (DE-588)4583995-5 gnd |
| topic_facet | Rechteckcode Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008811818&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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