Study on the Constructions of Balanced Optimal Binary Sequences with Period 4v (almost)

Sequences with optimal autocorrelation property have important roles in wireless communication, radar and cryptography. Therefore, in order to expand more ideal sequences that can be applied to communication systems, based on cyclotomy of order 2 and Chinese remainder theorem, three new constructions of balanced or almost balanced binary sequences of period T = 4v (v is odd prime) are presented in this paper. The periodic autocorrelation function of the constructed sequence satisfies: when v 3 (mod4), the out-of-phase autocorrelation value set of the sequence is {0, -4} or {0, 4, -4}; when v 1 (mod4), the corresponding value set is {0, 4, -4}. The existing range of balanced optimal binary sequences with period of 4v is extended by this method, so that more optimal sequences with good property can be provided for engineering applications.