On Some New Families of Almost Difference Sets Constructed From Cyclotomic Classes of Order 12

Abstract

Pseudorandom binary sequences with optimal balance and autocorrelation have many applications in stream cipher, communication, coding theory, etc. Constructing a binary sequences with three-level autocorrelation is equivalent to find the corresponding characteristic set of the sequences that should be an almost difference set. In this letter, we construct three new families of almost difference sets and two new families of difference sets from the cyclotomic classes of order twelve.