Multiphase Complementary Codes

A new class of complementary codes, similar to the complementary series of Golay but having multiphase elements, have been found to exist with specific complementary aperiodic complex autocorrelation functions. These new codes, called multiphase complementary codes, form a class of generalized complementary codes, of which the Golay complementary series can be considered to be a particular biphase subclass. Unlike Golay pairs, kernels of the new codes exist for odd length and can be synthesized. These new codes, like Golay pairs, are characterized by mathematical symmetries that may not be initially obvious because of apparent disorder. Multiphase complementary codes can be recursively expanded and used to form orthogonal or complementary sets of sequences. These complementary sets are not constrained to have even length or even cardinality. In addition, certain generalized Barker codes can also be utilized to form complementary sets with unique properties.