Binary Sequence/Array Pairs via Diference Set Pairs: A Recursive Approach
Binary array pairs with optimal/ideal correlation values and their algebraic counterparts \textquotedblleft difference set pairs\textquotedblright\;(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.
Arasu, K. T.,
& Puri, A.
(2017). Binary Sequence/Array Pairs via Diference Set Pairs: A Recursive Approach. Transactions on Combinatorics, 6 (3), 19-36.