Synthesis of cyclically orthogonal binary sequences of the same least period

The generation of cyclically orthogonal binary codes of the same least period is discussed. It will be shown that pairs of cyclically orthogonal binary sequences of length and least period
N = 2^{k}r
can be synthesized for all integers
k
and any nonprime odd integer r. The structure of these codes is self-evident from the synthesis; hence, codes of any given length of the indicated form are readily obtained. Bounds on the maximum possible number of mutually cyclically orthogonal binary sequences of the same least period are also presented.