Difference Sets and Sequences

Let G be a group of order v. A k-element subset D of G is called a (v,k,λ)-difference set in G if for any nonidentity element g∈G, there are λ pairs of elements d1,d2∈D such that d1d^−12=g. It is well-known that difference sets can be used to construct sequences used in digital communication. This paper is a survey on the recent developments of using difference sets and their variations to construct sequences with good auto-corrections or good cross-correlations.