Introduction to coding theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo
Springer
1998
|
| Edition: | 3., rev. and expanded ed. |
| Series: | Graduate texts in mathematics
86 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 218 - 222 |
| Physical Description: | XIV, 227 S. |
| ISBN: | 3540641335 |
Staff View
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| 245 | 1 | 0 | |a Introduction to coding theory |c J. H. van Lint |
| 250 | |a 3., rev. and expanded ed. | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo |b Springer |c 1998 | |
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| 490 | 1 | |a Graduate texts in mathematics |v 86 | |
| 500 | |a Literaturverz. S. 218 - 222 | ||
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Record in the Search Index
| _version_ | 1807773181504651264 |
|---|---|
| adam_text |
CONTENTS
PREFACE
TO
THE
THIRD
EDITION
.
V
PREFACE
TO
THE
SECOND
EDITION
.
VII
PREFACE
TO
THE
FIRST
EDITION
.
IX
CHAPTER
1
MATHEMATICAL
BACKGROUND
.
1
1.1.
ALGEBRA
.
1
1.2.
KRAWTCHOUK
POLYNOMIALS
.
14
1.3.
COMBINATORIAL
THEORY
.
17
1.4.
PROBABILITY
THEORY
.
19
CHAPTER
2
SHANNON
'
S
THEOREM
.
22
2.1.
INTRODUCTION
.
22
2.2.
SHANNON
'
S
THEOREM
.
27
2.3.
ON
CODING
GAIN
.
29
2.4.
COMMENTS
.
31
2.5.
PROBLEMS
.
32
CHAPTERS
LINEAR
CODES
.
33
3.1.
BLOCK
CODES
.
33
3.2.
LINEAR
CODES
.
35
3.3.
HAMMING
CODES
.
38
XII
CONTENTS
3.4,
MAJORITY
LOGIC
DECODING
.
39
3.5.
WEIGHT
ENUMERATORS
.
40
3.6.
THE
LEE
METRIC
.
42
3.7.
COMMENTS
.
44
3.8.
PROBLEMS
.
45
CHAPTER
4
SOME
GOOD
CODES
.
47
4.1.
HADAMARD
CODES
AND
GENERALIZATIONS
.
47
4.2.
THE
BINARY
GOLAY
CODE
.
48
4.3.
THE
TERNARY
GOLAY
CODE
.
51
4.4.
CONSTRUCTING
CODES
FROM
OTHER
CODES
.
51
4.5.
REED-MULLER
CODES
.
54
4.6.
KERDOCK
CODES
.
60
4.7.
COMMENTS
.
61
4.8.
PROBLEMS
.
62
CHAPTERS
BOUNDS
ON
CODES
.
64
5.1.
INTRODUCTION:
THE
GILBERT
BOUND
.
64
5.2.
UPPER
BOUNDS
.
67
5.3.
THE
LINEAR
PROGRAMMING
BOUND
.
74
5.4.
COMMENTS
.
78
5.5.
PROBLEMS
.
79
CHAPTER
6
CYCLIC
CODES
.
81
6.1.
DEFINITIONS
.
81
6.2.
GENERATOR
MATRIX
AND
CHECK
POLYNOMIAL
.
83
6.3.
ZEROS
OF
A
CYCLIC
CODE
.
84
6.4.
THE
IDEMPOTENT
OF
A
CYCLIC
CODE
.
86
6.5.
OTHER
REPRESENTATIONS
OF
CYCLIC
CODES
.
89
6.6.
BCH
CODES
.
91
6.7.
DECODING
BCH
CODES
.
98
6.8.
REED-SOLOMON
CODES
.
99
6.9.
QUADRATIC
RESIDUE
CODES
.
103
6.10.
BINARY
CYCLIC
CODES
OF
LENGTH
2N(N
ODD)
.
106
6.11.
GENERALIZED
REED-MULLER
CODES
.
108
6.12.
COMMENTS
.
110
6.13.
PROBLEMS
.
ILL
CHAPTER
7
PERFECT
CODES
AND
UNIFORMLY
PACKED
CODES
.
112
7.1.
LLOYD
'
S
THEOREM
.
112
7.2.
THE
CHARACTERISTIC
POLYNOMIAL
OF
A
CODE
.
115
CONTENTS
XIII
7.3.
UNIFORMLY
PACKED
CODES
.
118
7.4.
EXAMPLES
OF
UNIFORMLY
PACKED
CODES
.
120
7.5.
NONEXISTENCE
THEOREMS
.
123
7.6.
COMMENTS
.
127
7.7.
PROBLEMS
.
127
CHAPTERS
CODES
OVER
Z
4
.
128
8.1.
QUATERNARY
CODES
.
128
8.2.
BINARY
CODES
DERIVED
FROM
CODES
OVER
Z
4
.
129
8.3.
GALOIS
RINGS
OVER
2
4
.
132
8.4.
CYCLIC
CODES
OVER
Z
4
.
136
8.5.
PROBLEMS
.
138
CHAPTER
9
GOPPA
CODES
.
139
9.1.
MOTIVATION
.
139
9.2.
GOPPA
CODES
.
140
9.3.
THE
MINIMUM
DISTANCE
OF
GOPPA
CODES
.
142
9.4.
ASYMPTOTIC
BEHAVIOUR
OF
GOPPA
CODES
.
143
9.5.
DECODING
GOPPA
CODES
.
144
9.6.
GENERALIZED
BCH
CODES
.
145
9.7.
COMMENTS
.
146
9.8.
PROBLEMS
.
147
CHAPTER
10
ALGEBRAIC
GEOMETRY
CODES
.
148
10.1.
INTRODUCTION
.
148
10.2.
ALGEBRAIC
CURVES
.
149
10.3.
DIVISORS
.
155
10.4.
DIFFERENTIALS
ON
A
CURVE
.
156
10.5.
THE
RIEMANN-ROCH
THEOREM
.
158
10.6.
CODES
FROM
ALGEBRAIC
CURVES
.
160
10.7.
SOME
GEOMETRIC
CODES
.
162
10.8.
IMPROVEMENT
OF
THE
GILBERT-VARSHAMOV
BOUND
.
165
10.9.
COMMENTS
.
165
LO.LO.PROBLEMS
.
166
CHAPTER
11
ASYMPTOTICALLY
GOOD
ALGEBRAIC
CODES
.
167
11.1.
A
SIMPLE
NONCONSTRUCTIVE
EXAMPLE
.
167
11.2.
JUSTESEN
CODES
.
168
11.3.
COMMENTS
.
172
11.4.
PROBLEMS
.
172
XIV
CONTENTS
CHAPTER
12
ARITHMETIC
CODES
.
173
12.1.
AN
CODES
.
173
12.2.
THE
ARITHMETIC
AND
MODULAR
WEIGHT
.
175
12.3.
MANDELBAUM-BARROWS
CODES
.
179
12.4.
COMMENTS
.
180
12.5.
PROBLEMS
.
180
CHAPTER
13
CONVOLUTIONAL
CODES
.
181
13.1.
INTRODUCTION
.
181
13.2.
DECODING
OF
CONVOLUTIONAL
CODES
.
185
13.3.
AN
ANALOG
OF
THE
GILBERT
BOUND
FOR
SOME
CONVOLUTIONAL
CODES
.
187
13.4.
CONSTRUCTION
OF
CONVOLUTIONAL
CODES
FROM
CYCLIC
BLOCK
CODES
.
188
13.5.
AUTOMORPHISMS
OF
CONVOLUTIONAL
CODES
.
191
13.6.
COMMENTS
.
193
13.7.
PROBLEMS
.
194
HINTS
AND
SOLUTIONS
TO
PROBLEMS
.
195
REFERENCES
.
218
INDEX
.
223 |
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| spelling | Lint, Jacobus Hendricus van 1932-2004 Verfasser (DE-588)119136236 aut Introduction to coding theory J. H. van Lint 3., rev. and expanded ed. Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo Springer 1998 XIV, 227 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 86 Literaturverz. S. 218 - 222 Coding theory Codierung (DE-588)4070059-8 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Codierungstheorie (DE-588)4139405-7 s DE-604 Codierung (DE-588)4070059-8 s 3\p DE-604 Graduate texts in mathematics 86 (DE-604)BV000000067 86 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016912437&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lint, Jacobus Hendricus van 1932-2004 Introduction to coding theory Graduate texts in mathematics Coding theory Codierung (DE-588)4070059-8 gnd Codierungstheorie (DE-588)4139405-7 gnd |
| subject_GND | (DE-588)4070059-8 (DE-588)4139405-7 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Introduction to coding theory |
| title_auth | Introduction to coding theory |
| title_exact_search | Introduction to coding theory |
| title_exact_search_txtP | Introduction to coding theory |
| title_full | Introduction to coding theory J. H. van Lint |
| title_fullStr | Introduction to coding theory J. H. van Lint |
| title_full_unstemmed | Introduction to coding theory J. H. van Lint |
| title_short | Introduction to coding theory |
| title_sort | introduction to coding theory |
| topic | Coding theory Codierung (DE-588)4070059-8 gnd Codierungstheorie (DE-588)4139405-7 gnd |
| topic_facet | Coding theory Codierung Codierungstheorie Einführung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016912437&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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