Binary sequence/array pairs via diference set pairs: A recursive approach

Abstract

Binary array pairs with optimal/ideal correlation values and their algebraic counterparts textquotedblleft difference set pairstextquotedblright;(DSPs) in abelian groups are studied‎. ‎In addition to generalizing known 1-dimensional (sequences) examples‎, ‎we provide four new recursive constructions‎, ‎unifying previously obtained ones‎. ‎Any further advancements in the construction of binary sequences/arrays with optimal/ideal correlation values (equivalently cyclic/abelian difference sets) would give rise to richer classes of DSPs (and hence binary perfect array pairs)‎. ‎Discrete signals arising from DSPs find applications in cryptography‎, ‎CDMA systems‎, ‎radar and wireless communications‎.