Almost difference sets and their sequences with optimal autocorrelation

Almost difference sets have interesting applications in cryptography and co ding theory. In this paper, we give a well-rounded treatment of known famil ies of almost difference sets, establish relations between some difference sets and some almost difference sets, and determine the numerical multiplie r group of some families of almost difference sets. We also construct six n ew classes of almost difference sets, and four classes of binary sequences of period n equivalent to 0 (mod 4) with optimal autocorrelation. We have a lso obtained two classes of relative difference sets and four classes of di visible difference sets (DDSs). We also point out that a result due to Jung nickel can be used to construct almost difference sets and sequences of per iod 4l with optimal autocorrelation.