A class of optimal complete-complementary codes of different length

The class of complete-complementary code (CCC) sequence sets proposed by Suehiro and Hatori have ideal correlation properties which are very useful in suppressing multi-user interference when employed in spread spectrum communication systems and also provide reliable initial synchronization. Because of their nice correlation properties, they have a wide application. Though construction to the class of CCC sequence sets is important, study on their fundamental properties is equally important to characterize their behavior, which may yield some fruitful results. This paper discusses an interesting characteristic of the class of complete-complementary codes along with an iterative algorithm for the construction of a class of optimal complete-complementary codes. The algorithm generates an optimal [2^j+1, 2^j+1, 2^j+1]-CCC iteratively for each j = 1, 2, 3, .... Further, it is shown that the characteristic discussed can also be used to obtain a class of optimal complete-complementary codes of different length: an optimal [2N, 2N, {L + L_m}]-CCC can be obtained from [N, N, L]-CCC and [N, N, {L_m}]-CCC, the construction of which is the main result of the paper.