  Let $n_1$ and $n_2$ be two distinct primes with
$\mathrm{gcd}(n_1-1,n_2-1)=4$. In this paper, we compute the autocorrelation
values of generalized cyclotomic sequence of order $4$. Our results show that
this sequence can have very good autocorrelation property. We determine the
linear complexity and minimal polynomial of the generalized cyclotomic sequence
over $\mathrm{GF}(q)$ where $q=p^m$ and $p$ is an odd prime. Our results show
that this sequence possesses large linear complexity. So, the sequence can be
used in many domains such as cryptography and coding theory. We employ this
sequence of order $4$ to construct several classes of cyclic codes over
$\mathrm{GF}(q)$ with length $n_1n_2$. We also obtain the lower bounds on the
minimum distance of these cyclic codes.
