On the existence of periodic complementary binary sequences

Using the connection between periodic complementary binary sequences and difference families given by Bömer and Antweiler [2], we use number theoretic techniques to obtain necessary conditions for their existence when two or three sequences are involved. Our results provide theoretical proof for the nonexistence of PCS₃²⁰(a_i) and settle the open case PCS₂³⁶(a_i) of [2], negatively.Research partially supported by National Security Agency grant #MDA 904-90-H-4008.