Construction of binary sequences with low correlation via multiplicative quadratic character over finite fields of odd characteristics

In literature, there are several methods to construct Gold sequences. One of the constructions is via the trace function from extension field of $\mathbb {F}_{2}$ . Estimation of correlation of this construction is based on number of rational points of elliptic curves. In this article, we generalize this construction from finite fields of even characteristic to odd characteristics by using multiplicative quadratic character. Again, estimation of correlation of this construction is based on number of rational points of elliptic curves. Thus, we obtain binary sequences which have more flexibility on length while still possessing low correlation property. Moreover, some of the sequences are optimally balanced.