  During the last two decades, many kinds of periodic sequences with good
pseudo-random properties have been constructed from classical and generalized
cyclotomic classes, and used as keystreams for stream ciphers and secure
communications. Among them are a family DH-GCS$_{d}$ of generalized cyclotomic
sequences on the basis of Ding and Helleseth's generalized cyclotomy, of length
$pq$ and order $d=\mathrm{gcd}(p-1,q-1)$ for distinct odd primes $p$ and $q$.
The linear complexity (or linear span), as a valuable measure of
unpredictability, is precisely determined for DH-GCS$_{8}$ in this paper. Our
approach is based on Edemskiy and Antonova's computation method with the help
of explicit expressions of Gaussian classical cyclotomic numbers of order $8$.
Our result for $d=8$ is compatible with Yan's low bound $(pq-1)/2$ of the
linear complexity for any order $d$, which means high enough to resist security
attacks of the Berlekamp-Massey algorithm. Finally, we include SageMath codes
to illustrate the validity of our result by examples.
