Commutative algebra methods for coding theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2024]
|
| Schriftenreihe: | De Gruyter studies in mathematics
Volume 97 |
| Schlagworte: | |
| Online-Zugang: | https://www.degruyter.com/isbn/9783111212920 Inhaltsverzeichnis |
| Beschreibung: | IX, 264 Seiten Illustrationen 24 cm x 17 cm |
| ISBN: | 9783111212920 3111212920 |
Internformat
MARC
| LEADER | 00000nam a22000008cb4500 | ||
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| 003 | DE-604 | ||
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| 020 | |a 3111212920 |9 3-11-121292-0 | ||
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| 044 | |a gw |c XA-DE-BE | ||
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| 100 | 1 | |a Tohǎneanu, Ştefan Ovidiu I. |e Verfasser |0 (DE-588)1333533462 |4 aut | |
| 245 | 1 | 0 | |a Commutative algebra methods for coding theory |c Ştefan Ovidiu I. Tohǎneanu |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2024] | |
| 300 | |a IX, 264 Seiten |b Illustrationen |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics |v Volume 97 | |
| 650 | 0 | 7 | |a Kommutative Algebra |0 (DE-588)4164821-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Codierung |0 (DE-588)4141834-7 |2 gnd |9 rswk-swf |
| 653 | |a Mindestabstand | ||
| 653 | |a Dimension eines Ideals | ||
| 653 | |a Duale lineare Formen | ||
| 653 | |a Bewertungscode | ||
| 653 | |a Minimum distance | ||
| 653 | |a height of an ideal | ||
| 653 | |a dual linear forms | ||
| 653 | |a fat points | ||
| 653 | |a evaluation code | ||
| 653 | |a socle degree. | ||
| 689 | 0 | 0 | |a Algebraische Codierung |0 (DE-588)4141834-7 |D s |
| 689 | 0 | 1 | |a Kommutative Algebra |0 (DE-588)4164821-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 9783111214795 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 9783111215389 |
| 830 | 0 | |a De Gruyter studies in mathematics |v Volume 97 |w (DE-604)BV000005407 |9 97 | |
| 856 | 4 | 2 | |m X:MVB |u https://www.degruyter.com/isbn/9783111212920 |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035115071&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035115071 | |
Datensatz im Suchindex
| _version_ | 1816956184899354624 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
-
1
2
2.1
2.1.1
2.1.2
2.1.3
2.1.4
2.1.5
2.1.6
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
2.2.6
2.2.7
2.2.8
2.2.9
2.2.10
2.3
2.3.1
2.3.2
2.3.3
2.3.4
PRELIMINARIES
-
5
CODING
THEORY
-
5
GENERALITIES
-
5
NEAREST
NEIGHBOR
ALGORITHM
AND
PERFECT
CODES
-
8
BOUNDS
-
10
GENERALIZED
HAMMING
WEIGHTS
-
11
WEIGHT
DISTRIBUTION
AND
WEIGHT
ENUMERATOR
-
12
CYCLIC
CODES
-
13
COMMUTATIVE
ALGEBRA
-
17
GENERALITIES
-
17
CHAIN
CONDITIONS
ON
MODULES
-
19
GRADED
RINGS
AND
MODULES,
RINGS
OF
POLYNOMIALS
-
21
RINGS
OF
FRACTIONS
-
23
PRIMARY
DECOMPOSITION
-
24
DIMENSION
THEORY
-
26
SOME
ALGEBRAIC
GEOMETRY
-
28
HILBERT
FUNCTION
AND
DEGREE
-
36
GRADED
FREE
RESOLUTIONS
-
39
MONOMIAL
ORDERS
-
51
COMBINATORICS
-
61
SIMPLICIAL
COMPLEXES
-
61
MATROIDS
-
65
HYPERPLANE
ARRANGEMENTS
-
67
WEIGHT
ENUMERATORS
AND
HYPERPLANE
ARRANGEMENTS
-
71
3
3.1
3.2
3.2.1
3.2.2
3.3
3.3.1
3.3.2
3.3.3
3.4
IDEALS
GENERATED
BY
FOLD
PRODUCTS
OF
LINEAR
FORMS
-
73
IDEALS
GENERATED
BY
A-FOLD
PRODUCTS
OF
LINEAR
FORMS
-
74
THE
DE
BOER-PELLIKAAN
METHOD
FOR
COMPUTING
MINIMUM
DISTANCE
-
76
MINIMUM
DISTANCE
AND
HEIGHTS
OF
IDEALS
-
76
GENERALIZED
HAMMING
WEIGHTS
-
79
PROJECTIVE
CODEWORDS
OF
MINIMUM
WEIGHT
-
81
PARITY-CHECK
MATRIX
APPROACH
-
83
PRIMARY DECOMPOSITION
APPROACH
-
84
MINIMAL
CODEWORDS
-
86
PRIMARY
DECOMPOSITION
OF
IDEALS
GENERATED
BY
A-FOLD
PRODUCTS
OF
LINEAR
FORMS
-
89
3.4.1
3.4.2
THE
GENERAL
CASE
-
92
STAR
CONFIGURATIONS
-
98
3.5
AN
ERROR-CORRECTION
ALGORITHM
-
100
3.6
LINEAR
CODES
INTERPOLATION
-
103
3.6.1
SUBSPACE
ARRANGEMENTS
AND
SUBCODES
-
105
3.6.2
INTERPOLATING
FAT
POINTS
IN
P-1
-
106
3.6.3
INTERPOLATING
REDUCED
POINTS
WITH
GIVEN
REGULARITY
-
109
3.7
MINIMUM
DISTANCE
AS
THE
INITIAL
DEGREE
-
116
3.7.1
THE
FITTING
MODULE
OF
A
LINEAR
CODE
-
117
3.7.2
A
BINARY
ASSOCIATED
GRADED
ALGEBRA
-
119
4
FAT
POINTS
DEFINING
LINEAR
CODES
-
122
4.1
GEOMETRY
OF
MINIMUM
DISTANCE
-
123
4.2
THE
MINIMUM
DISTANCE
AND
THE
INITIAL
DEGREE
OF
POINTS
-
126
4.2.1
THE
REDUCED
CASE
-
127
4.2.2
THE
FAT-POINTS
CASE
-
132
4.3
THE
MINIMUM
DISTANCE
AND
THE
MINIMUM
SOCLE
DEGREE
-
134
4.3.1
THE
CASE
OF
REDUCED
COMPLETE
INTERSECTIONS
-
140
4.4
ADDITIONAL
RESULTS
FOR
SPECIFIC
SITUATIONS
-
143
4.4.1
MINIMUM
DISTANCE
AND
THE
INDEX
OF
NILPOTENCY
-
143
4.4.2
CONFIGURATIONS
OF
POINTS
ASSOCIATED
TO
STEINER
SYSTEMS
-
146
4.4.3
FAT
POINTS
HAVING
COMPLETE
INTERSECTION
SUPPORT
-
149
5
EVALUATION
CODES
-
154
5.1
REED-MULLER
CODES
-
156
5.1.1
ALGEBRAIC
GEOMETRIC
AND
TORIC
CODES
-
161
5.1.2
AFFINE
VARIETY
CODES
-
164
5.2
EVALUATION
CODES
-
171
5.2.1
EVALUATION
CODES
OF
MINIMUM
DISTANCE
ONE
-
173
5.2.2
POINTS
IN
GENERAL
LINEAR
POSITION
-
175
5.2.3
GENERALIZED
HAMMING
WEIGHTS
OF
EVALUATION
CODES
-
179
5.2.4
CODES
CONSTRUCTED
FROM
GRAPHS
-
183
5.3
PARAMETERIZED
CODES
-
186
5.3.1
DEFINING
IDEALS
OF
TORIC
SETS
-
187
5.3.2
TECHNIQUES
FOR
PARAMETERIZED
CODES
-
190
5.3.3
CODES
PARAMETERIZED
BY
PROJECTIVE
TORUS
-
193
5.3.4
CODES
PARAMETERIZED
BY
GRAPHS
-
195
5.3.5
VERONESE
TYPE
CODES
-
200
5.4
AFFINE
CARTESIAN
CODES
-
201
5.4.1
PROJECTIVE
NESTED
CARTESIAN
CODES
-
204
5.5
THE
DUAL
OF
AN
EVALUATION
CODE
-
205
5.5.1
SELF-DUAL
CODES
AND
GALE
TRANSFORMS
-
209
5.5.2
INITIAL
DEGREE
OF
INVERSE
SYSTEMS
-
211
6
6.1
6.1.1
6.1.2
6.2
6.2.1
6.2.2
6.2.3
ADDITIONAL
TOPICS
-
212
MINIMUM
DISTANCE
AND
INITIAL
DEGREES
OF
COMBINATORIAL
ALGEBRAS
-
213
STANLEY-REISNER
RING
OF
MATROIDS
OF
GENERATOR
MATRICES
-
214
THE
ORLIK-TERAO
ALGEBRA
-
220
MINIMUM
DISTANCE
FUNCTIONS
-
226
FOOTPRINT
FUNCTION
-
229
THE
V-NUMBER
OF
A
GRADED
IDEAL
-
233
THE
CAYLEY-BACHARACH
CONJECTURES
AND
THE
MINIMUM
DISTANCE
FUNCTION
-
237
6.2.4
RELATIVE
GENERALIZED
MINIMUM
DISTANCE
FUNCTIONS
-
240
BIBLIOGRAPHY
-
245
INDEX
OF
NOTATIONS
-
253
INDEX
-
257 |
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| author | Tohǎneanu, Ştefan Ovidiu I. |
| author_GND | (DE-588)1333533462 |
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| author_role | aut |
| author_sort | Tohǎneanu, Ştefan Ovidiu I. |
| author_variant | ş o i t şoi şoit |
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| bvnumber | BV049773948 |
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| illustrated | Illustrated |
| indexdate | 2024-11-28T09:00:47Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783111212920 3111212920 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035115071 |
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| owner | DE-29T |
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| physical | IX, 264 Seiten Illustrationen 24 cm x 17 cm |
| publishDate | 2024 |
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| record_format | marc |
| series | De Gruyter studies in mathematics |
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| spelling | Tohǎneanu, Ştefan Ovidiu I. Verfasser (DE-588)1333533462 aut Commutative algebra methods for coding theory Ştefan Ovidiu I. Tohǎneanu Berlin ; Boston De Gruyter [2024] IX, 264 Seiten Illustrationen 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics Volume 97 Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Algebraische Codierung (DE-588)4141834-7 gnd rswk-swf Mindestabstand Dimension eines Ideals Duale lineare Formen Bewertungscode Minimum distance height of an ideal dual linear forms fat points evaluation code socle degree. Algebraische Codierung (DE-588)4141834-7 s Kommutative Algebra (DE-588)4164821-3 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 9783111214795 Erscheint auch als Online-Ausgabe, EPUB 9783111215389 De Gruyter studies in mathematics Volume 97 (DE-604)BV000005407 97 X:MVB https://www.degruyter.com/isbn/9783111212920 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035115071&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20240120 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Tohǎneanu, Ştefan Ovidiu I. Commutative algebra methods for coding theory De Gruyter studies in mathematics Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Codierung (DE-588)4141834-7 gnd |
| subject_GND | (DE-588)4164821-3 (DE-588)4141834-7 |
| title | Commutative algebra methods for coding theory |
| title_auth | Commutative algebra methods for coding theory |
| title_exact_search | Commutative algebra methods for coding theory |
| title_full | Commutative algebra methods for coding theory Ştefan Ovidiu I. Tohǎneanu |
| title_fullStr | Commutative algebra methods for coding theory Ştefan Ovidiu I. Tohǎneanu |
| title_full_unstemmed | Commutative algebra methods for coding theory Ştefan Ovidiu I. Tohǎneanu |
| title_short | Commutative algebra methods for coding theory |
| title_sort | commutative algebra methods for coding theory |
| topic | Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Codierung (DE-588)4141834-7 gnd |
| topic_facet | Kommutative Algebra Algebraische Codierung |
| url | https://www.degruyter.com/isbn/9783111212920 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035115071&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
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