Difference Sets, Sequences and their Correlation Properties

1. Front Matter

   Pages i-viii

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2. Perfect Ternary Arrays

   • K. T. Arasu, J. F. Dillon

   Pages 1-15

3. Stream Ciphers and Correlation

   • K. Brincat, F. C. Piper, P. R. Wild

   Pages 17-44

4. Error Correcting Codes, Correlation and Quantum Entanglement

   • A. R. Calderbank

   Pages 45-84

5. A Unified Approach to Difference Sets with gcd(V,N) > 1

   • James A. Davis, Jonathan Jedwab

   Pages 85-112

6. Codes, Correlations and Power Control in OFDM

   • James A. Davis, Jonathan Jedwab, Kenneth G. Paterson

   Pages 113-132

7. Kasami Power Functions, Permutation Polynomials and Cyclic Difference Sets

   • Hans Dobbertin

   Pages 133-158

8. Construction of Signals with Favorable Correlation Properties

   • S. W. Golomb

   Pages 159-194

9. Codes and Sequences Over ℤ4 — A Tutorial Overview

   • Tor Helleseth, P. Vijay Kumar

   Pages 195-225

10. The Merit Factor of Binary Sequences

    • Tom Høholdt

    Pages 227-237

11. Lander’s Tables are Complete!

    • Joel E. Iiams

    Pages 239-257

12. Difference Sets: An Introduction

    • Dieter Jungnickel, Alexander Pott

    Pages 259-295

13. Applications of Difference Sets to the Aperture Design in Multielement Systems in Radio Science and Astronomy

    • L. E. Kopilovich

    Pages 297-330

14. Constructive Representation Theoretic Methods and Non-Abelian Difference Sets

    • Robert A. Liebler

    Pages 331-352

15. Survey of Results on Signal Patterns for Locating One or Multiple Targets

    • Oscar Moreno

    Pages 353-368

16. Sequence Design for CDMA Systems

    • Hans D. Schotten

    Pages 369-392

17. Bent Functions and Coding Theory

    • Jacques Wolfmann

    Pages 393-418

18. Recent Results on Difference Sets with Classical Parameters

    • Qing Xiang

    Pages 419-437

19. Back Matter

    Pages 439-448

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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.

• Permutation
• Phase
• Signal
• algebra
• coding
• coding theory
• patterns
• radio
• sets
• tables
• combinatorics

• Otto-von-Guericke-Universität, Magdeburg, Germany

  A. Pott

• University of Southern California, Los Angeles, USA

  P. V. Kumar

• University of Bergen, Norway

  T. Helleseth

• University of Augsburg, Germany

  D. Jungnickel

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