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  • 1
    Online Resource
    Online Resource
    Finite Fields and Their Applications : Character Sums and Polynomials (2013)
    Berlin [u.a.] : de Gruyter
    Details
    UID:
    gbv_1656033054
    Format: Online-Ressource (PDF-Version: XI, 274 S.)
    ISBN: 9783110283600
    Series Statement: Radon Series on Computational and Applied Mathematics 11
    Content: Biographical note: Pascale Charpin, INRIA, Le Chesnay, France;Alexander Pott, Otto-von-Guericke-University Magdeburg, Germany; Arne Winterhof, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria.
    Content: This book contains nine survey papers on topics in fnite fields and their applications, in particular on character sums and polynomials. The articles are based on the invited talks ofa RICAM-Workshop held at the St. Wolfgang Federal Institute for Adult Education in Strobl, Austria, September 2-7, 2012, by the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences.
    Content: This book contains nine survey papers on topics in fnite fields and their applications, in particular on character sums and polynomials. The articles are based on the invited talks ofa RICAM-Workshop held at the St. Wolfgang Federal Institute for Adult Education in Strobl, Austria, September 2-7, 2012, by the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences
    Additional Edition: ISBN 9783110282405
    Additional Edition: ISBN 9783110283600
    Additional Edition: Erscheint auch als Druck-Ausgabe Finite fields and their applications Berlin [u.a.] : De Gruyter, 2013 ISBN 9783110283617
    Additional Edition: ISBN 3110282402
    Additional Edition: ISBN 9783110282405
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-11-028360-0
    Language: English
    Subjects: Mathematics
    RVK:
    SK 910
    Keywords: Galois-Feld ; Konferenzschrift
    DOI: 10.1515/9783110283600
    URL: Volltext
    URL: Volltext  (lizenzpflichtig)
    URL: lizenzpflichtig
    URL: Cover
    URL: Inhaltstext
    URL: Cover
    Author information: Charpin, Pascale
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    UB Potsdam
  • 2
    Online Resource
    Online Resource
    Finite fields and their applications : character sums and polynomials (2013)
    Berlin ; : De Gruyter,
    Details
    UID:
    edoccha_9959233106502883
    Format: 1 online resource (288 p.)
    Edition: 1st ed.
    Series Statement: Radon series on computational and applied mathematics, v. 11
    Content: This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
    Note: Based on the RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials, held at the Federal Institute for Adult Education in Strobl, Austria, September 2-7, 2012. , Front matter -- , Preface -- , Contents -- , Character Sums and Polyphase Sequence Families with Low Correlation, Discrete Fourier Transform (DFT), and Ambiguity / , Measures of Pseudorandomness / , Existence Results for Finite Field Polynomials with Specified Properties / , Incidence Structures, Codes, and Galois Geometries / , Special Mappings of Finite Fields / , On The Classification of Perfect Nonlinear (PN) and Almost Perfect Nonlinear (APN) Monomial Functions / , Finite Fields and Quasirandom Points / , Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects / , Additive Combinatorics over Finite Fields: New Results and Applications / , Index -- , Backmatter , Issued also in print. , English
    Additional Edition: ISBN 3-11-028360-3
    Additional Edition: ISBN 3-11-028240-2
    Language: English
    DOI: 10.1515/9783110283600
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    Charité
  • 3
    Online Resource
    Online Resource
    Finite fields and their applications : character sums and polynomials (2013)
    Berlin ; : De Gruyter,
    Details
    UID:
    edocfu_9959233106502883
    Format: 1 online resource (288 p.)
    Edition: 1st ed.
    Series Statement: Radon series on computational and applied mathematics, v. 11
    Content: This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
    Note: Based on the RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials, held at the Federal Institute for Adult Education in Strobl, Austria, September 2-7, 2012. , Front matter -- , Preface -- , Contents -- , Character Sums and Polyphase Sequence Families with Low Correlation, Discrete Fourier Transform (DFT), and Ambiguity / , Measures of Pseudorandomness / , Existence Results for Finite Field Polynomials with Specified Properties / , Incidence Structures, Codes, and Galois Geometries / , Special Mappings of Finite Fields / , On The Classification of Perfect Nonlinear (PN) and Almost Perfect Nonlinear (APN) Monomial Functions / , Finite Fields and Quasirandom Points / , Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects / , Additive Combinatorics over Finite Fields: New Results and Applications / , Index -- , Backmatter , Issued also in print. , English
    Additional Edition: ISBN 3-11-028360-3
    Additional Edition: ISBN 3-11-028240-2
    Language: English
    DOI: 10.1515/9783110283600
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    FU Berlin
  • 4
    Online Resource
    Online Resource
    Finite Fields and Their Applications : Character Sums and Polynomials (2013)
    Details
    UID:
    almahu_9947359998102882
    Format: Online-Ressource (XI, 274 S.)
    ISBN: 9783110282405 (print)
    Series Statement: Radon Series on Computational and Applied Mathematics 11
    Content: Biographical note: Pascale Charpin, INRIA, Le Chesnay, France;Alexander Pott, Otto-von-Guericke-University Magdeburg, Germany; Arne Winterhof, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria.
    Content: Main description: This book contains nine survey papers on topics in fnite fields and their applications, in particular on character sums and polynomials. The articles are based on the invited talks ofa RICAM-Workshop held at the St. Wolfgang Federal Institute for Adult Education in Strobl, Austria, September 2-7, 2012, by the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences.
    Content: This book contains nine survey papers on topics in fnite fields and their applications, in particular on character sums and polynomials. The articles are based on the invited talks ofa RICAM-Workshop held at the St. Wolfgang Federal Institute for Adult Education in Strobl, Austria, September 2-7, 2012, by the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences
    Note: Description based upon print version of record , 4.1 Sequences from the Additive Group of ZN and the Additive Group of Zp4.1.1 Frank-Zadoff-Chu (FZC) Sequences; 4.1.2 Another Class for Zn; 4.1.3 Sequences from Fp Additive Characters; 4.2 Sequences from Fp Multiplicative Characters; 4.3 Sequences from Fq Additive Characters; 4.4 Sequences from Fq Multiplicative Characters; 4.5 Sequences Defined by Indexing Field Elements Alternatively; 5 Sequences with Low Degree Polynomials; 5.1 Methods for Generating Signal Sets from a Single Sequence; 5.2 Sequences with Low Odd Degree Polynomials. , 5 Connection between Pseudorandom Measures6 Constructions; 7 Family Measures; 8 Linear Complexity; 9 Multidimensional Theory; 10 Extensions; Existence Results for Finite Field Polynomials with Specified Properties; 1 Introduction; 2 A Survey of Known Results; 2.1 Normal Bases; 2.2 Primitive Normal Bases; 2.3 Prescribed Coefficients; 2.4 Primitive Polynomials: Prescribed Coefficients; 2.5 Primitive Normal Polynomials: Prescribed Coefficients; 3 A Survey of Methodology and Techniques; 3.1 Basic Approach; 3.2 A p-adic Approach to Coefficient Constraints; 3.3 The Sieving Technique; 4 Conclusion. , 5.2.1 Fq Additive Sequences with Low Odd Degree Polynomials5.2.2 Fq Multiplicative Sequences with Low Odd Degree Polynomials; 5.3 Sequences from Power Residue and Sidel'nikov Sequences; 5.3.1 Interleaved Structure of Sidel'nikov Sequences; 5.3.2 Sequences from Linear and/or Quadratic/Inverse Polynomials; 5.4 Sequences from Hybrid Characters; 5.4.1 Sequences Using Weil Representation and Their Generalizations; 5.4.2 Generalization to Fq Hybrid Sequences; 5.5 A New Construction; 6 Two-Level Autocorrelation Sequences and Double Exponential Sums; 6.1 Prime Two-Level Autocorrelation Sequences. , 6.2 Hadamard Transform, Second-Order Decimation-Hadamard Transform, and Hadamard Equivalence6.3 Conjectures on Ternary 2-Level Autocorrelation Sequences; 7 Some Open Problems; 7.1 Current Status of the Conjectures on Ternary 2-Level Autocorrelation; 7.2 Possibility of Multiplicative Sequences with Low Autocorrelation; 7.3 Problems in Four Alternative Classes of Sequences and the General Hybrid Construction; 8 Conclusions; Measures of Pseudorandomness; 1 Introduction; 2 Definition of the Pseudorandom Measures; 3 Typical Values of Pseudorandom Measures; 4 Minimum Values of Pseudorandom Measures. , Incidence Structures, Codes, and Galois Geometries. , Preface; Character Sums and Polyphase Sequence Families with Low Correlation, Discrete Fourier Transform (DFT), and Ambiguity; 1 Introduction; 2 Basic Definitions and Concepts; 2.1 Notations; 2.2 Polynomial Functions over Fq; 2.3 Characters of Finite Fields; 2.4 The Weil Bounds on Character Sums; 3 Correlation, DFT, and Ambiguity Functions; 3.1 Operators on Sequences; 3.2 Correlation Functions; 3.3 Ambiguity Functions; 3.4 Convolution and Correlation; 3.5 Optimal Correlation, DFT, and Ambiguity; 4 Polyphase Sequences for Three Metrics.
    Additional Edition: ISBN 9783110283600
    Additional Edition: ISBN 9783110283617
    Language: English
    Keywords: Electronic books
    DOI: 10.1515/9783110283600
    URL: http://dx.doi.org/10.1515/9783110283600
    URL: http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110283600&searchTitles=true
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  • 5
    Online Resource
    Online Resource
    Finite Fields and Their Applications : Character Sums and Polynomials (2013)
    Berlin/Boston :De Gruyter,
    Details
    UID:
    edocfu_9958354072602883
    Format: 1 online resource(xi,274p.) : , illustrations.
    Edition: Electronic reproduction. Berlin/Boston : De Gruyter. Mode of access: World Wide Web.
    Edition: System requirements: Web browser.
    Edition: Access may be restricted to users at subscribing institutions.
    ISBN: 9783110283600
    Series Statement: Radon Series on Computational and Applied Mathematics; 11
    Content: This book contains nine survey papers on topics in finite fields and their applications, in particular on character sums and polynomials. The articles are based on the invited talks ofa RICAM-Workshop held at the St. Wolfgang Federal Institute for Adult Education in Strobl, Austria, September 2-7, 2012, by the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences.
    Note: Frontmatter -- , Preface -- , Contents -- , Character Sums and Polyphase Sequence Families with Low Correlation, Discrete Fourier Transform (DFT), and Ambiguity / , Measures of Pseudorandomness / , Existence Results for Finite Field Polynomials with Specified Properties / , Incidence Structures, Codes, and Galois Geometries / , Special Mappings of Finite Fields / , On The Classification of Perfect Nonlinear (PN) and Almost Perfect Nonlinear (APN) Monomial Functions / , Finite Fields and Quasirandom Points / , Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects / , Additive Combinatorics over Finite Fields: New Results and Applications / , Index -- , Backmatter. , Also available in print edition. , In English.
    Additional Edition: ISBN 9783110282405
    Additional Edition: ISBN 9783110283617
    Language: English
    DOI: 10.1515/9783110283600
    URL: https://doi.org/10.1515/9783110283600
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  • 6
    Online Resource
    Online Resource
    Finite Fields and Their Applications : Character Sums and Polynomials (2013)
    Berlin ; : De Gruyter,
    Details
    UID:
    almahu_9949462261202882
    Format: 1 online resource (274 p.)
    ISBN: 9783110283600 , 9783110238570
    Series Statement: Radon Series on Computational and Applied Mathematics , 11
    Content: This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
    Note: Frontmatter -- , Preface -- , Contents -- , Character Sums and Polyphase Sequence Families with Low Correlation, Discrete Fourier Transform (DFT), and Ambiguity -- , Measures of Pseudorandomness -- , Existence Results for Finite Field Polynomials with Specified Properties -- , Incidence Structures, Codes, and Galois Geometries -- , Special Mappings of Finite Fields -- , On The Classification of Perfect Nonlinear (PN) and Almost Perfect Nonlinear (APN) Monomial Functions -- , Finite Fields and Quasirandom Points -- , Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects -- , Additive Combinatorics over Finite Fields: New Results and Applications -- , Index -- , Backmatter , Issued also in print. , Mode of access: Internet via World Wide Web. , In English.
    In: DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
    In: DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
    In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
    In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013, De Gruyter, 9783110317350
    In: E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013, De Gruyter, 9783110317282
    In: E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013, De Gruyter, 9783110317275
    In: Radon Series on Applied Mathematics eBook-Package, De Gruyter, 9783110647174
    Additional Edition: ISBN 9783110282405
    Language: English
    DOI: 10.1515/9783110283600
    URL: https://doi.org/10.1515/9783110283600
    URL: https://www.degruyter.com/isbn/9783110283600
    URL: Cover
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