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.