Coding theory and number theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2003
|
| Series: | Mathematics and its applications
554 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 148 S. Ill. |
| ISBN: | 1402012039 |
Staff View
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Record in the Search Index
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| adam_text | CODING THEORY AND NUMBER THEORY BY TOYOKAZU HIRAMATSU HOSEI UNIVERSITY,
TOKYO, JAPAN AND GIINTER KOHLER WTIRZBURG UNIVERSITY, WTIRZBURG, GERMANY
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS PREFACE
IX 1. LINEAR CODES 1 1 CODING THEORY 1 2 LINEAR CODES 4 3 CYCLIC CODES 7
4 FINITE FIELDS 13 5 BCH CODES 14 2. DIOPHANTINE EQUATIONS AND CYCLIC
CODES 17 1 DIAGONAL EQUATIONS OVER FINITE FIELDS 17 2 THE NUMBER OF
SOLUTIONS AND WEIGHT DISTRIBUTIONS OF CYCLIC CODES 18 3. ELLIPTIC
CURVES, HECKE OPERATORS AND WEIGHT DISTRIBUTION OF CODES 23 1 ELLIPTIC
CURVES OVER FINITE FIELDS 23 1.1 THE GROUP LAW 24 1.2 HASSE S THEOREM 27
2 MODULAR FORMS AND HECKE OPERATORS 29 2.1 SL2{7I) AND ITS CONGRUENCE
SUBGROUPS 29 2.2 THE UPPER HALF-PLANE 30 2.3 MODULAR FORMS AND CUSP
FORMS 30 2.4 HECKE OPERATORS 32 3 WEIGHT DISTRIBUTION OF LINEAR CODES 35
3.1 THE MACWILLIAMS IDENTITIES AND DELSARTE S THEOREM 35 3.2 THE WEIGHT
DISTRIBUTION OF THE MELAS CODES 39 VI CODING THEORY AND NUMBER THEORY 4.
ALGEBRAIC-GEOMETRIC CODES AND MODULAR CURVE CODES 1 2 3 4 5 CLASSICAL
GOPPA CODES 1.1 1.2 THE BASIC IDEA BASIC PROPERTIES OF F(L,G) ALGEBRAIC
CURVES 2.1 2.2 THE 3.1 3.2 AFFINE VARIETIES AND PROJECTIVE VARIETIES
DIVISORS OF ALGEBRAIC CURVES ZETA FUNCTIONS OF CURVES AND RATIONAL
POINTS BASIC PROPERTIES OF THE ZETA FUNCTIONS MAXIMUM NUMBER OF RATIONAL
POINTS ALGEBRAIC-GEOMETRIC CODES 4.1 4.2 ALGEBRAIC-GEOMETRIC CODES OF
THE FIRST KIND ALGEBRAIC-GEOMETRIC CODES OF THE SECOND KIND MODULAR
CURVES AND CODES 5.1 5.2 5.3 5. THETA CODES 1 2 3 MODULAR CURVES AND
THEIR REDUCTION MODULO P PROOF OF THEOREM 4.8 ASYMPTOTIC BOUNDS
FUNCTIONS AND SELF-DUAL LATTICES AND CODES 1.1 1.2 1.3 1.4 LATTICES
CONSTRUCTING LATTICES FROM BINARY CODES EXAMPLES THE LATTICES ASSOCIATED
TO A CODE AND THE DUAL CODE THETA FUNCTIONS AND WEIGHT DISTRIBUTIONS 2.1
2.2 THE THETA FUNCTION OF A LATTICE THE MACWILLIAMS IDENTITY DOUBLY-EVEN
SELF-DUAL CODES 3.1 3.2 3.3 APPENDIX THE THE WEIGHT ENUMERATOR OF
DOUBLY-EVEN SELF-DUAL CODES THE EXTENDED GOLAY CODE THE LEECH LATTICE J
KLOOSTERMAN CODES AND DISTRIBUTION OF THE WEIGHTS 1 INTRODUCTION 49 49
49 51 52 52 55 58 58 61 62 62 65 66 67 69 72 77 77 77 81 83 91 92 92 101
105 105 108 112 116 117 117 CONTENTS VII 2 MELAS CODE AND KLOOSTERMAN
SUMS 119 3 HYPER-KLOOSTERMAN CODE 122 4 QUASI-CYCLIC PROPERTY 126 5
WEIGHT DISTRIBUTION 128 6 MINIMUM DISTANCE OF C M (Q) 133 7 A
DIVISIBILITY THEOREM FOR HAMMING WEIGHTS 136 REFERENCES 141 INDEX 145
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| indexdate | 2024-07-09T19:13:03Z |
| institution | BVB |
| isbn | 1402012039 |
| language | English |
| lccn | 2003044749 |
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| physical | XI, 148 S. Ill. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Hiramatsu, Toyokazu Verfasser aut Coding theory and number theory by Toyokazu Hiramatsu and Günter Köhler Dordrecht [u.a.] Kluwer Acad. Publ. 2003 XI, 148 S. Ill. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 554 Coding theory Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 s DE-604 Zahlentheorie (DE-588)4067277-3 s Köhler, Günter Sonstige oth Mathematics and its applications 554 (DE-604)BV008163334 554 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010282328&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hiramatsu, Toyokazu Coding theory and number theory Mathematics and its applications Coding theory Number theory Zahlentheorie (DE-588)4067277-3 gnd Codierungstheorie (DE-588)4139405-7 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4139405-7 |
| title | Coding theory and number theory |
| title_auth | Coding theory and number theory |
| title_exact_search | Coding theory and number theory |
| title_full | Coding theory and number theory by Toyokazu Hiramatsu and Günter Köhler |
| title_fullStr | Coding theory and number theory by Toyokazu Hiramatsu and Günter Köhler |
| title_full_unstemmed | Coding theory and number theory by Toyokazu Hiramatsu and Günter Köhler |
| title_short | Coding theory and number theory |
| title_sort | coding theory and number theory |
| topic | Coding theory Number theory Zahlentheorie (DE-588)4067277-3 gnd Codierungstheorie (DE-588)4139405-7 gnd |
| topic_facet | Coding theory Number theory Zahlentheorie Codierungstheorie |
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