General limit theorem for n phase Barker sequences

Let N_L be the total number of normalised n phase Barker sequences of length L as n→∞. A general limit theorem describing a fundamental relationship between the existence of certain uniform Barker sequences and the finiteness of N_L is presented. As a corollary, the limit theorem of Zhang and Golomb is extended from length 19 to 31. The insight gained from the author´s limit theorem is that if any n phase Barker sequence of length L exists with L>31, it is very likely that there are an infinite number of them