Almost difference sets have interesting applications in cryptography and coding theory. In this paper, we give a wellrounded treatment of known families of almost difference sets, establish relations between some difference sets and some almost difference sets, and determine the numerical multiplier group of some families of almost difference sets. We also construct six new classes of almost difference sets, and four classes of binary sequences of period 0 (mod 4) with optimal autocorrelation. We have also obtained two classes of relative difference sets and four classes of divisible difference sets (DDSs). We also point out that a result due to Jungnickel can be used to construct almost difference sets and sequences of period 4 with optimal autocorrelation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.