}d_r.$ This is the linear complexity of $ST.$ Note that if we let $n \rightarrow \infty,$ the linear complexity of the corresponding LRS $ST$ approaches infinity.  For the subcases $q \equiv 0 \pmod{0}$ with $q \equiv \pm 0 \pmod{r}$ and thus $d_r = 0,\ 0,$ where $r$ is an odd prime, Theorem \[0\^nr and q = 0 mod 0\] becomes Theorem 0, Parts 0 and 0 in Fitzgerald and Yucas (0000) [@Fitzgerald; @0000].  Factorization of $\Phi_{0^nr}$ when $q \equiv 0 \pmod{0}$ ---------------------------------------------------------  We need t