Difference sets and sequences

Abstract

Let G be a group of order ν. A k-element subset D of G is called a (ν,k,λ)- difference set in G if for any nonidentity element g ∈ G, there are λ pairs of elements d 1;d 2 ∈ D such that d 1d -1 2 = 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.