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.
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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.
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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.
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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.
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Incidence Structures, Codes, and Galois Geometries.
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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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