Periodic complementary binary sequences

Existence conditions and recursive construction procedures for sets of periodic complementary binary sequences are given. Relationships to sets of aperiodic complementary binary sequences and to perfect binary arrays, whose two-dimensional periodic autocorrelation function is a delta function, are noted. The connections of periodic complementary binary sequences and difference families are given. Sets of periodic complementary binary sequences, which result from computer search, are presented. A diagram showing what is currently known about the existence of periodic complementary binary sequences with P⩽12 sequences of N⩽50 elements is given