Description 
1 online resource (xi, 274 pages) 
Series 
Radon Series on Computational and Applied Mathematics 

Radon series on computational and applied mathematics

Contents 
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 

4.1 Sequences from the Additive Group of ZN and the Additive Group of Zp; 4.1.1 FrankZadoffChu (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 

5.2.1 Fq Additive Sequences with Low Odd Degree Polynomials; 5.2.2 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 TwoLevel Autocorrelation Sequences and Double Exponential Sums; 6.1 Prime TwoLevel Autocorrelation Sequences 

6.2 Hadamard Transform, SecondOrder DecimationHadamard Transform, and Hadamard Equivalence; 6.3 Conjectures on Ternary 2Level Autocorrelation Sequences; 7 Some Open Problems; 7.1 Current Status of the Conjectures on Ternary 2Level 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 

5 Connection between Pseudorandom Measures; 6 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 padic Approach to Coefficient Constraints; 3.3 The Sieving Technique; 4 Conclusion 
Summary 
"This book is based on the invited talks of the "RICAMWorkshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 27, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasiMonte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. 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."Publisher's website 
Bibliography 
Includes bibliographical references and index 
Notes 
Print version record 
Subject 
Finite fields (Algebra)  Congresses


Mathematics  Congresses


Telecommunication systems  Congresses


Electronics  Congresses


MATHEMATICS  Algebra  Intermediate.


Electronics.


Finite fields (Algebra)


Mathematics.


Telecommunication systems.

Genre/Form 
Conference papers and proceedings.

Form 
Electronic book

Author 
Charpin, P. (Pascale), 1949


Pott, Alexander, 1961


Winterhof, Arne

ISBN 
9783110283600 

3110283603 

1299723578 

9781299723573 

9783110282405 

3110282402 
