Finite fields and their applications: character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012]
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Tagungsbericht Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston, Mass.
<<De>> Gruyter
2013
|
| Schriftenreihe: | Radon series on computational and applied mathematics
11 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XI, 374 S. 25 cm |
| ISBN: | 9783110282405 |
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Datensatz im Suchindex
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|---|---|
| adam_text |
IMAGE 1
CONTENTS
PREFACE V
GUANG GONG
CHARACTER SUMS AND POLYPHASE SEQUENCE FAMILIES WITH LOW CORRELATION,
DISCRETE FOURIER TRANSFORM (DFT), AND AMBIGUITY 1
1 INTRODUCTION 1
2 BASIC DEFINITIONS AND CONCEPTS 2
2.1 NOTATIONS 2
2.2 POLYNOMIAL FUNCTIONS OVER 3
2.3 CHARACTERS OF FINITE FIELDS 4
2.4 THE WEIL BOUNDS ON CHARACTER SUMS 4
3 CORRELATION, DFT, AND AMBIGUITY FUNCTIONS - 5
3.1 OPERATORS ON SEQUENCES 5
3.2 CORRELATION FUNCTIONS 6
3.3 AMBIGUITY FUNCTIONS 8
3.4 CONVOLUTION AND CORRELATION 10
3.5 OPTIMAL CORRELATION, DFT, AND AMBIGUITY 10
4 POLYPHASE SEQUENCES FOR THREE METRICS 11
4.1 SEQUENCES FROM THE ADDITIVE GROUP OF I N AND
THE ADDITIVE GROUP OF ~L V 11 4.1.1 FRANK-ZADOFF-CHU (FZC) SEQUENCES 11
4.1.2 ANOTHER CLASS FOR 13
4.1.3 SEQUENCES FROM F P ADDITIVE CHARACTERS 13
4.2 SEQUENCES FROM F P MULTIPLICATIVE CHARACTERS 13
4.3 SEQUENCES FROM FQ ADDITIVE CHARACTERS 15
4.4 SEQUENCES FROM MULTIPLICATIVE CHARACTERS 17
4.5 SEQUENCES DEFINED BY INDEXING FIELD ELEMENTS ALTERNATIVELY 20 5
SEQUENCES WITH LOW DEGREE POLYNOMIALS 22
5.1 METHODS FOR GENERATING SIGNAL SETS FROM A SINGLE SEQUENCE 22
5.2 SEQUENCES WITH LOW ODD DEGREE POLYNOMIALS 23
5.2.1 FQ ADDITIVE SEQUENCES WITH LOW ODD DEGREE POLYNOMIALS - 23
5.2.2 FQ MULTIPLICATIVE SEQUENCES WITH LOW ODD DEGREE POLYNOMIALS
5.3 SEQUENCES FROM POWER RESIDUE AND SIDEL'NIKOV SEQUENCES 2 6
5.3.1 INTERLEAVED STRUCTURE OF SIDEL'NIKOV SEQUENCES 2 6
5.3.2 SEQUENCES FROM LINEAR AND/OR QUADRATIC/INVERSE POLYNOMIALS 2
5.4 SEQUENCES FROM HYBRID CHARACTERS 29
5.4.1 SEQUENCES USINGWEIL REPRESENTATION AND THEIR GENERALIZATIONS -
5.4.2 GENERALIZATION TO FQ HYBRID SEQUENCES 30
5.5 A NEW CONSTRUCTION 32
HTTP://D-NB.INFO/1029258910
IMAGE 2
VIII
CONTENTS
6 TWO-LEVEL AUTOCORRELATION SEQUENCES AND DOUBLE EXPONENTIAL
SUMS 33
6.1 PRIME TWO-LEVEL AUTOCORRELATION SEQUENCES 33
6.2 HADAMARD TRANSFORM, SECOND-ORDER DECIMATION-HADAMARD TRANSFORM,
AND HADAMARD EQUIVALENCE 34
6.3 CONJECTURES ON TERNARY 2-LEVEL AUTOCORRELATION SEQUENCES 35
7 SOME OPEN PROBLEMS 37
7.1 CURRENT STATUS OF THE CONJECTURES ON TERNARY 2-LEVEL
AUTOCORRELATION 37
7.2 POSSIBILITY OF MULTIPLICATIVE SEQUENCES WITH LOW AUTOCORRELATION - 3
8
7.3 PROBLEMS IN FOUR ALTERNATIVE CLASSES OF SEQUENCES AND THE GENERAL
HYBRID CONSTRUCTION 3 8
8 CONCLUSIONS 3 8
KATALIN GYARMATI
MEASURES OF PSEUDORANDOMNESS 43
1 INTRODUCTION 43
2 DEFINITION OF THE PSEUDORANDOM MEASURES 4 4
3 TYPICAL VALUES OF PSEUDORANDOM M E A S U R E S - 4 6
4 MINIMUM VALUES OF PSEUDORANDOM MEASURES 47
5 CONNECTION BETWEEN PSEUDORANDOM MEASURES 4 9
6 CONSTRUCTIONS 50
7 FAMILY MEASURES 52
8 LINEAR COMPLEXITY 54
9 MULTIDIMENSIONALTHEORY 56
10 EXTENSIONS 57
SOPHIE HUCZYNSKA
EXISTENCE RESULTS FOR FINITE FIELD POLYNOMIALS WITH SPECIFIED PROPERTIES
- 65
1 INTRODUCTION 65
2 A SURVEY OF KNOWN RESULTS 6 6
2.1 NORMAL BASES 67
2.2 PRIMITIVE NORMAL BASES 6 8
2.3 PRESCRIBED COEFFICIENTS 70
2.4 PRIMITIVE POLYNOMIALS: PRESCRIBED COEFFICIENTS 70
2.5 PRIMITIVE NORMAL POLYNOMIALS: PRESCRIBED COEFFICIENTS 73
3 A SURVEY OF METHODOLOGY AND TECHNIQUES 75
3.1 BASIC APPROACH 76
3.2 A P-ADIC APPROACH TO COEFFICIENT CONSTRAINTS 78
3.3 THE SIEVINGTECHNIQUE 8 1
4 CONCLUSION 8 3
IMAGE 3
CONTENTS IX
DIETER JUNGNICKEL
INCIDENCE STRUCTURES, CODES, AND GALOIS GEOMETRIES 8 9
1 INTRODUCTION 8 9
2 GALOIS CLOSED CODES 9 1
3 EXTENSION CODES OF SIMPLEX AND FIRST-ORDER REED-MULLER CODES - 93
4 SIMPLE INCIDENCE STRUCTURES AND THEIR CODES 97
5 EMBEDDING THEOREMS 9 9
6 DESIGNS WITH CLASSICAL PARAMETERS 105
7 TWO-WEIGHT CODES 108
8 STEINER SYSTEMS 109
9 CONFIGURATIONS 111
10 CONCLUSION AND OPEN PROBLEMS 113
GOHAR M. KYUREGHYAN
SPECIAL MAPPINGS OF FINITE FIELDS 117
1 INTRODUCTION 117
2 DIFFERENT NOTIONS FOR OPTIMAL NON-LINEARITY 120
2.1 ALMOST PERFECT NONLINEAR (APN) MAPPINGS 121
2.2 BENT AND ALMOST BENT (AB) MAPPINGS 124
3 FUNCTIONS WITH A LINEAR STRUCTURE - 125
4 CROOKED MAPPINGS 128
5 PLANAR MAPPINGS 130
6 SWITCHING CONSTRUCTION 133
7 PRODUCTS OF LINEARIZED POLYNOMIALS 137
FERNANDO HERNANDO AND GARY MCGUIRE
ON THE CLASSIFICATION OF PERFECT NONLINEAR (PN) AND ALMOST PERFECT
NONLINEAR (APN)
MONOMIAL FUNCTIONS 145
1 INTRODUCTION 145
2 BACKGROUND AND MOTIVATION 146
2.1 PN AND PLANAR FUNCTIONS 146
2.2 APN FUNCTIONS 148
3 OUTLINE OF APN FUNCTIONS CLASSIFICATION PROOF 149
3.1 SINGULARITIES IN APN CASE 151
3.2 A WARM-UP CASE 153
4 PN FUNCTIONS CLASSIFICATION PROOF: ANALYSIS OF SINGULARITIES 154
4.1 SINGULAR POINTS IN CASE (B.L) 156
4.2 SINGULAR POINTS AT INFINITY 157
4.3 THE MULTIPLICITIES 159
4.4 FURTHER ANALYSIS 159
4.5 TYPE(I) 161
IMAGE 4
X - CONTENTS
4.6 TYPE (III) 161
4.7 TYPE (II) 161
5 CASE (B.L): ASSUMING B T ( X , Y ) IRREDUCIBLE OVER FP 162
6 CASE (B.L): ASSUMING B T { X , Y ) NOT IRREDUCIBLE OVER FP 164
HARALD NIEDERREITER
FINITE FIELDS AND QUASIRANDOM POINTS 169
1 INTRODUCTION 169
2 GENERAL BACKGROUND 170
3 GENERAL CONSTRUCTION PRINCIPLES 173
4 THE COMBINATORICS OF NETS 177
5 DUALITY THEORY 179
6 SPECIAL CONSTRUCTIONS OF NETS 181
6.1 POLYNOMIAL LATTICES 181
6.2 HYPERPLANE NETS 183
6.3 NETS OBTAINED FROM GLOBAL FUNCTION FIELDS 185
7 SPECIAL CONSTRUCTIONS OF (T, S)-SEQUENCES 187
7.1 FAURE SEQUENCES AND NIEDERREITER SEQUENCES 188
7.2 SEQUENCES OBTAINED FROM GLOBAL FUNCTION FIELDS "189
7.3 SEQUENCES WITH FINITE-ROW GENERATING MATRICES 192
ALINA OSTAFE ITERATIONS OF RATIONAL FUNCTIONS: SOME ALGEBRAIC AND
ARITHMETIC ASPECTS 197
1 INTRODUCTION 197
1.1 BACKGROUND 197
1.2 NOTATION 198
1.3 ITERATIONS 198
2 DISTRIBUTION OF ELEMENTS, DEGREE GROWTH AND REPRESENTATION 199
2.1 EXPONENTIAL SUMS AND LINEAR COMBINATIONS OF ITERATES 199
2.2 GENERIC MULTIVARIATE POLYNOMIALS 201
2.3 SYSTEMS WITH SLOW DEGREE GROWTH 203
2.4 EXPONENTIAL DEGREE GROWTH, BUT SPARSE REPRESENTATION 206
2.5 REPRESENTATION OF ITERATES 207
2.6 DELIGNE AND DWORK-REGULAR POLYNOMIALS 2 0 8
2.7 DISTRIBUTION IN PRIME AND POLYNOMIAL TIMES 209
3 STRUCTURE OF RATIONAL FUNCTION MAPS 210
3.1 TRAJECTORY LENGTH AND PERIODIC STRUCTURE 210
3.2 GRAPH OF RATIONAL FUNCTION MAPS 212
3.3 COMMON COMPOSITES AND INTERSECTION OF ORBITS 213
4 GEOMETRIC PROPERTIES OF ORBITS 215
4.1 DIAMETER OF ORBITS 215
4.2 CONVEX HULL OF TRAJECTORIES 217
IMAGE 5
CONTENTS
XI
5 STABILITY, ABSOLUTE IRREDUCIBILITY AND COPRIMALITY 217
5.1 MOTIVATION 217
5.2 STABLE UNIVARIATE P O L Y N O M I A L S - 218
5.3 ON THE GROWTH OF THE NUMBER OF IRREDUCIBLE FACTORS 220
5.4 STABLE MULTIVARIATE POLYNOMIALS 222
5.5 COPRIMALITY OF ITERATES 224
6 MORE PROBLEMS 224
6.1 MULTIPLICATIVE I N D E P E N D E N C E - 224
6.2 COMPLETE POLYNOMIALS 225
IGOR E. SHPARLINSKI
ADDITIVE COMBINATORICS OVER FINITE FIELDS: NEW RESULTS AND APPLICATIONS
233
1 INTRODUCTION 233
2 NOTATION 235
3 ESTIMATES FROM ARITHMETIC COMBINATORICS 236
3.1 CLASSICAL SUM-PRODUCT PROBLEM 236
3.2 MULTIFOLD SUM-PRODUCT P R O B L E M - 238
3.3 SUM-INVERSION ESTIMATES 239
3.4 EQUATIONS OVER FINITE FIELDS WITH VARIABLES FROM ARBITRARY SETS 241
3.5 INCIDENCE BOUNDS 243
3.6 POLYNOMIAL AND OTHER NONLINEAR FUNCTIONS ON SETS 245
3.7 STRUCTURED SETS 247
3.8 ELLIPTIC CURVE ANALOGUES 249
3.9 MATRIX ANALOGUES 252
4 APPLICATIONS 253
4.1 EXPONENTIAL AND CHARACTER SUMS 253
4.2 WARING, ERDOS-GRAHAM AND OTHER ADDITIVE PROBLEMS IN FINITE
FIELDS 256
4.3 INTERSECTIONS OF ALMOST ARITHMETIC AND GEOMETRIC PROGRESSIONS 258
4.4 EXPONENTIAL CONGRUENCE 260
4.5 HIDDEN SHIFTED POWER PROBLEM 261
4.6 SUM-PRODUCT ESTIMATES AND MULTIPLICATIVE ORDERS OF Y AND Y + Y ~ L
IN FINITE FIELDS 261
4.7 EXPANSION OF DYNAMICAL SYSTEMS 262
INDEX 273 |
| any_adam_object | 1 |
| author2 | Charpin, Pascale |
| author2_role | edt |
| author2_variant | p c pc |
| author_GND | (DE-588)141092181 |
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| dewey-full | 512.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.32 |
| dewey-search | 512.32 |
| dewey-sort | 3512.32 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Conference Proceeding Book |
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| spelling | Finite fields and their applications character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012] [RICAM, Johann Radon Institute for Computational and Applied Mathematics ; ÖAW, Austrian Academy of Sciences]. Ed. by Pascale Charpin ... Berlin ; Boston, Mass. <<De>> Gruyter 2013 XI, 374 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Radon series on computational and applied mathematics 11 Literaturangaben Galois-Feld (DE-588)4155896-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2012 Strobl gnd-content Galois-Feld (DE-588)4155896-0 s DE-604 Charpin, Pascale (DE-588)141092181 edt Bundesinstitut für Erwachsenenbildung Sonstige (DE-588)403501-X oth Workshop on Finite Fields and Their Applications: Character Sums and Polynomials 2012 Strobl Sonstige (DE-588)103571082X oth Radon series on computational and applied mathematics 11 (DE-604)BV023335470 11 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4221501&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026166929&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Finite fields and their applications character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012] Radon series on computational and applied mathematics Galois-Feld (DE-588)4155896-0 gnd |
| subject_GND | (DE-588)4155896-0 (DE-588)1071861417 |
| title | Finite fields and their applications character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012] |
| title_auth | Finite fields and their applications character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012] |
| title_exact_search | Finite fields and their applications character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012] |
| title_full | Finite fields and their applications character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012] [RICAM, Johann Radon Institute for Computational and Applied Mathematics ; ÖAW, Austrian Academy of Sciences]. Ed. by Pascale Charpin ... |
| title_fullStr | Finite fields and their applications character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012] [RICAM, Johann Radon Institute for Computational and Applied Mathematics ; ÖAW, Austrian Academy of Sciences]. Ed. by Pascale Charpin ... |
| title_full_unstemmed | Finite fields and their applications character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012] [RICAM, Johann Radon Institute for Computational and Applied Mathematics ; ÖAW, Austrian Academy of Sciences]. Ed. by Pascale Charpin ... |
| title_short | Finite fields and their applications |
| title_sort | finite fields and their applications character sums and polynomials invited talks of the ricam workshop on finite fields and their application character sums and polynomials held at the federal institute for adult education bifeb in strobl austria from september 2 7 2012 |
| title_sub | character sums and polynomials ; [invited talks of the RICAM-Workshop on Finite Fields and Their Application: Character Sums and Polynomials held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2 - 7, 2012] |
| topic | Galois-Feld (DE-588)4155896-0 gnd |
| topic_facet | Galois-Feld Konferenzschrift 2012 Strobl |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4221501&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026166929&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023335470 |
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