Periodic complementary binary sequences and combinatorial optimization algorithms

We establish a new formalism for problems pertaining to the periodic autocorrelation function of finite sequences, which is suitable for Combinatorial Optimization methods. This allows one to bring to bear powerful Combinatorial Optimization methods in a wide array of problems that can be formulated via the periodic autocorrelation function. Using this new formalism we solve all remaining open problems regarding periodic complementary binary sequences, in the context of the Bömer and Antweiler diagram and thus complete the program that they started in 1990.