Linear recurrence relations over finite fields:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bergen
Univ.
1966
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 212 S. graph. Darst. |
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MARC
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Record in the Search Index
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| adam_text | CONTENTS
Chapter I; Galois fields.
1. Some fundamental concepts 1
2. Finite fields 5
3. Irreducible and primitive polynomials 11
Chapter II: Linear recurrence.
1. Feedback shift registers 18
2. The difference equation 23
3. The matrix method; non canonical registers .... 25
4. Reverse and symmetric sequences 30
5. Recurrence over arbitrary finite fields 33
6. Historical survey 35
Chapter III: The difference equation.
1. The solution space 39
2. Fundamental identities 42
3. The classical method 46
4. The method of Ward and Hall 51
5. The method of Peterson and Laksov 52
6. The method of Zierler 55
Chapter IV: The cycle structure.
1. The minimum polynomial 62
2.. Regular sequences 65
3» Sequences of determinants 68
4.. Sum and intersection 75
5» Repeated factors 80
6. The general case 84
7. Multiplication of sequences 90
Chapter V: Distribution problems.
1. Multipliers and blocks 98
2. Definition of multigrams 103
3. Structure and distribution of multigrams ...... 108
4. Equations for the numbers of zeros 113
5. Equidistribution of elements in sequences ..... 121
6. Decimation of periodic sequences 126
7. Invariance under decimation 132
8. Hall s homomorphism 138
9. The unit sequences 142
10. The power sum sequence s 145
11. Addition and subtraction formulas 150
Chapter VI: Binary sequences.
1. The number of cycles 154
2. Binary complementation 156
3. Autocorrelation 161
4. Golomb s randomness postulates 169
5. Difference sets and difference cycles 172
Chapter VII: The matrix method.
1. Introduction 178
2. Vector recurrence and sequence rank 180
3. The general theory 186
4. Some special cases 191
5. On the number of matrices 198
Tables 201
Bibliography 207
Index 211
|
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| author | Selmer, Ernst S. 1920- |
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| indexdate | 2024-07-09T17:29:24Z |
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| spelling | Selmer, Ernst S. 1920- Verfasser (DE-588)123984874 aut Linear recurrence relations over finite fields Bergen Univ. 1966 212 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lineare Rekursion (DE-588)4402273-6 gnd rswk-swf Schieberegisterfolge gnd rswk-swf Schieberegisterfolge f DE-604 Lineare Rekursion (DE-588)4402273-6 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005997021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Selmer, Ernst S. 1920- Linear recurrence relations over finite fields Lineare Rekursion (DE-588)4402273-6 gnd |
| subject_GND | (DE-588)4402273-6 |
| title | Linear recurrence relations over finite fields |
| title_auth | Linear recurrence relations over finite fields |
| title_exact_search | Linear recurrence relations over finite fields |
| title_full | Linear recurrence relations over finite fields |
| title_fullStr | Linear recurrence relations over finite fields |
| title_full_unstemmed | Linear recurrence relations over finite fields |
| title_short | Linear recurrence relations over finite fields |
| title_sort | linear recurrence relations over finite fields |
| topic | Lineare Rekursion (DE-588)4402273-6 gnd |
| topic_facet | Lineare Rekursion Schieberegisterfolge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005997021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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