Elements of algebraic coding theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall
1996
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Chapman & Hall mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 254 S. |
| ISBN: | 0412573806 |
Internformat
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Datensatz im Suchindex
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| adam_text | IMAGE 1
ELEMENTS OF ALGEBRAIC
CODING THEORY
L. R. VERMANI
PROFESSOR OF MATHEMATICS KURUKSHETRA UNIVERSITY KURUKSHETRA, INDIA
CHAPMAN & HALL LONDON * WEINHEIM * NEW YORK * TOKYO * MELBOURNE * MADRAS
IMAGE 2
CONTENTS
PREFACE VII
1 GROUP CODES 1
1.1 ELEMENTARY PROPERTIES 1
1.2 MATRIX ENCODING TECHNIQUES 8
1.3 GENERATOR AND PARITY CHECK MATRICES 14
2 POLYNOMIAL CODES 24
2.1 DEFINITION OF VECTOR SPACE AND POLYNOMIAL RING 24
2.2 POLYNOMIAL CODES 26
2.3 GENERATOR AND PARITY CHECK MATRICES - GENERAL CASE 34
3 HAMMING CODES 39
3.1 BINARY REPRESENTATION OF NUMBERS 39
3.2 HAMMING CODES 41
4 FINITE FIELDS AND BCH CODES 47
*4.1 FINITE FIELDS 47
4.2 SOME EXAMPLES OF PRIMITIVE POLYNOMIALS 62
4.3 BOSE-CHAUDHURI-HOCQUENGHEM CODES 65
5 LINEAR CODES 81
5.1 GENERATOR AND PARITY CHECK MATRICES 81
5.2 DUAL CODE OF A LINEAR CODE 87
5.3 WEIGHT DISTRIBUTION OF THE DUAL CODE OF A BINARY LINEAR CODE 97 5.4
NEW CODES OBTAINED FROM GIVEN CODES 102
6 CYCLIC CODES 107
6.1 CYCLIC CODES 107
6.2 CHECK POLYNOMIAL 111
IMAGE 3
VI CONTENTS
6.3 BCH AND HAMMING CODES AS CYCLIC CODES 114
6.4 NON-BINARY HAMMING CODES 119
6.5 IDEMPOTENTS 129
6.6 SOME SOLVED EXAMPLES AND AN INVARIANCE PROPERTY 131
6.7 CYCLIC CODES AND GROUP ALGEBRAS 135
6.8 SELF DUAL BINARY CYCLIC CODES 137
7 FACTORIZATION OF POLYNOMIALS 140
7.1 FACTORS OF X -L 140
7.2 FACTORIZATION THROUGH CYCLOTOMIC COSETS 143
7.3 BERLEKAMP S ALGORITHM FOR FACTORIZATION OF POLYNOMIALS 149 7.4
BERLEKAMP S ALGORITHM - A SPECIAL CASE 157
8 QUADRATIC RESIDUE CODES 172
8.1 INTRODUCTION 172
8.2 SOME EXAMPLES OF QUADRATIC RESIDUE CODES 176
8.3 EXTENDED QUADRATIC RESIDUE CODES AND DISTANCE PROPERTIES 180 8.4
IDEMPOTENTS OF QUADRATIC RESIDUE CODES 194
8.5 SOME EXAMPLES 202
9 MAXIMUM DISTANCE SEPARABLE CODES 208
9.1 NECESSARY AND SUFFICIENT CONDITIONS FOR MDS CODES 208 9.2 THE WEIGHT
DISTRIBUTION OF MDS CODES 215
9.3 AN EXISTENCE PROBLEM 218
9.4 REED-SOLOMON CODES 220
10 AUTOMORPHISM GROUP OF A CODE 223
10.1 AUTOMORPHISM GROUP OF A BINARY CODE 223
10.2 AUTOMORPHISM GROUP OF A NON-BINARY CODE 229
10.3 AUTOMORPHISM GROUP - ITS RELATION WITH MINIMUM DISTANCE 234
11 HADAMARD MATRICES AND HADAMARD CODES 242
11.1 HADAMARD MATRICES 242
11.2 HADAMARD CODES 248
BIBLIOGRAPHY 251
INDEX 253
|
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| indexdate | 2024-07-09T18:03:17Z |
| institution | BVB |
| isbn | 0412573806 |
| language | English |
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| physical | VIII, 254 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Chapman & Hall |
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| series2 | Chapman & Hall mathematics series |
| spelling | Vermani, Lekh R. Verfasser aut Elements of algebraic coding theory L. R. Vermani 1. ed. London [u.a.] Chapman & Hall 1996 VIII, 254 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall mathematics series Algebra gtt Coding theory Algebraische Codierung (DE-588)4141834-7 gnd rswk-swf Algebraische Codierung (DE-588)4141834-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007405945&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vermani, Lekh R. Elements of algebraic coding theory Algebra gtt Coding theory Algebraische Codierung (DE-588)4141834-7 gnd |
| subject_GND | (DE-588)4141834-7 |
| title | Elements of algebraic coding theory |
| title_auth | Elements of algebraic coding theory |
| title_exact_search | Elements of algebraic coding theory |
| title_full | Elements of algebraic coding theory L. R. Vermani |
| title_fullStr | Elements of algebraic coding theory L. R. Vermani |
| title_full_unstemmed | Elements of algebraic coding theory L. R. Vermani |
| title_short | Elements of algebraic coding theory |
| title_sort | elements of algebraic coding theory |
| topic | Algebra gtt Coding theory Algebraische Codierung (DE-588)4141834-7 gnd |
| topic_facet | Algebra Coding theory Algebraische Codierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007405945&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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