Optimal binary signature sets under cyclic shifts

We derive new bounds on the periodic (cyclic) total squared correlation (PTSC) of binary antipodal signature sets for any number of signatures K and any signature length L. Optimal designs that achieve the new bounds are then developed for several (K, L) cases. As an interesting side result, binary periodic complementary sequence (PCS) sets are seen to be PTSC optimal. Furthermore, as an example that arguably may be against common expectation, it is seen that neither the Gold nor the Kasami sets are PTSC optimal; the optimal sets provided herein are in this sense better suited for asynchronous and/or multipath code-division multiplexing applications