Ebook: Difference Sets, Sequences and their Correlation Properties

The explanation of the formal duality of Kerdock and Preparata codes is one of the outstanding results in the field of applied algebra in the last few years. This result is related to the discovery of large sets of quad­ riphase sequences over Z4 whose correlation properties are better than those of the best binary sequences. Moreover, the correlation properties of sequences are closely related to difference properties of certain sets in (cyclic) groups. It is the purpose of this book to illustrate the connection between these three topics. Most articles grew out of lectures given at the NATO Ad­ vanced Study Institute on "Difference sets, sequences and their correlation properties". This workshop took place in Bad Windsheim (Germany) in August 1998. The editors thank the NATO Scientific Affairs Division for the generous support of this workshop. Without this support, the present collection of articles would not have been realized.

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The explanation of the formal duality of Kerdock and Preparata codes - one of the outstanding recent results in applied algebra - is related to the discovery of large sets of quadriphase sequences over Z₄ whose correlation properties are better than those of the best binary sequences. Moreover, the correlation properties of sequences are closely related to difference properties of certain sets in (cyclic) groups.
Most of the articles collected here contain descriptions of the connection between difference sets, sequences and correlation properties of sequences. There are two more elementary introductory articles: an introduction to difference sets (by two of the editors), and an introduction to the correlation of sequences (by Solomon Golomb).

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The explanation of the formal duality of Kerdock and Preparata codes - one of the outstanding recent results in applied algebra - is related to the discovery of large sets of quadriphase sequences over Z₄ whose correlation properties are better than those of the best binary sequences. Moreover, the correlation properties of sequences are closely related to difference properties of certain sets in (cyclic) groups.
Most of the articles collected here contain descriptions of the connection between difference sets, sequences and correlation properties of sequences. There are two more elementary introductory articles: an introduction to difference sets (by two of the editors), and an introduction to the correlation of sequences (by Solomon Golomb).
Content:
Front Matter....Pages i-viii
Perfect Ternary Arrays....Pages 1-15
Stream Ciphers and Correlation....Pages 17-44
Error Correcting Codes, Correlation and Quantum Entanglement....Pages 45-84
A Unified Approach to Difference Sets with gcd(V,N) > 1....Pages 85-112
Codes, Correlations and Power Control in OFDM....Pages 113-132
Kasami Power Functions, Permutation Polynomials and Cyclic Difference Sets....Pages 133-158
Construction of Signals with Favorable Correlation Properties....Pages 159-194
Codes and Sequences Over ?4 — A Tutorial Overview....Pages 195-225
The Merit Factor of Binary Sequences....Pages 227-237
Lander’s Tables are Complete!....Pages 239-257
Difference Sets: An Introduction....Pages 259-295
Applications of Difference Sets to the Aperture Design in Multielement Systems in Radio Science and Astronomy....Pages 297-330
Constructive Representation Theoretic Methods and Non-Abelian Difference Sets....Pages 331-352
Survey of Results on Signal Patterns for Locating One or Multiple Targets....Pages 353-368
Sequence Design for CDMA Systems....Pages 369-392
Bent Functions and Coding Theory....Pages 393-418
Recent Results on Difference Sets with Classical Parameters....Pages 419-437
Back Matter....Pages 439-448

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The explanation of the formal duality of Kerdock and Preparata codes - one of the outstanding recent results in applied algebra - is related to the discovery of large sets of quadriphase sequences over Z₄ whose correlation properties are better than those of the best binary sequences. Moreover, the correlation properties of sequences are closely related to difference properties of certain sets in (cyclic) groups.
Most of the articles collected here contain descriptions of the connection between difference sets, sequences and correlation properties of sequences. There are two more elementary introductory articles: an introduction to difference sets (by two of the editors), and an introduction to the correlation of sequences (by Solomon Golomb).
Content:
Front Matter....Pages i-viii
Perfect Ternary Arrays....Pages 1-15
Stream Ciphers and Correlation....Pages 17-44
Error Correcting Codes, Correlation and Quantum Entanglement....Pages 45-84
A Unified Approach to Difference Sets with gcd(V,N) > 1....Pages 85-112
Codes, Correlations and Power Control in OFDM....Pages 113-132
Kasami Power Functions, Permutation Polynomials and Cyclic Difference Sets....Pages 133-158
Construction of Signals with Favorable Correlation Properties....Pages 159-194
Codes and Sequences Over ?4 — A Tutorial Overview....Pages 195-225
The Merit Factor of Binary Sequences....Pages 227-237
Lander’s Tables are Complete!....Pages 239-257
Difference Sets: An Introduction....Pages 259-295
Applications of Difference Sets to the Aperture Design in Multielement Systems in Radio Science and Astronomy....Pages 297-330
Constructive Representation Theoretic Methods and Non-Abelian Difference Sets....Pages 331-352
Survey of Results on Signal Patterns for Locating One or Multiple Targets....Pages 353-368
Sequence Design for CDMA Systems....Pages 369-392
Bent Functions and Coding Theory....Pages 393-418
Recent Results on Difference Sets with Classical Parameters....Pages 419-437
Back Matter....Pages 439-448
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