Difference Sets, Sequences and Their Correlation Properties

the long version

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).