  The autocorrelation and the linear complexity of a key stream sequence in a
stream cipher are important cryptographic properties. Many sequences with these
good properties have interleaved structure, three classes of binary sequences
of period $4N$ with optimal autocorrelation values have been constructed by
Tang and Gong based on interleaving certain kinds of sequences of period $N$.
In this paper, we use the interleaving technique to construct a binary sequence
with the optimal autocorrelation of period $2N$, then we calculate its
autocorrelation values and its distribution, and give a lower bound of linear
complexity. Results show that these sequences have low autocorrelation and the
linear complexity satisfies the requirements of cryptography.
