M-ary mutually orthogonal complementary gold codes

A method to obtain large sets of periodic conjugate symmetric sequences with perfect periodic autocorrelation functions is presented. Each of these perfect sequences can be transformed into two real sequences which are perfectly orthogonal for any cyclic shift. In this way, mutually orthogonal complementary (MOC) sequences derived from bipolar Gold codes can be transformed into M-ary MOC Gold codes. Ternary MOC Gold codes are the simpler implementation case and exist in large number. These Ternary MOC Gold codes provide a greater immunity to multi-path interferences than other codes, like Hadamard codes, Orthogonal Gold codes, Gold codes, and Complementary Golay codes, when a periodic or aperiodic autocorrelation function is used for asynchronous bit detection.