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Finite fields and their applications : character sums and polynomials /
"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 a...
| Clasificación: | Libro Electrónico |
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| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
©2013.
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| Colección: | Radon series on computational and applied mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 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.
- 5.2.1 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 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 Equivalence; 6.3 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.
- 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 p-adic Approach to Coefficient Constraints; 3.3 The Sieving Technique; 4 Conclusion.