Orthogonal cycle systems with cycle length less than 10

An $H$-decomposition of a graph $G$ is a partition of the edge set of $G$ into subsets, where each subset induces a copy of the graph $H$. A $k$-orthogonal $H$-decomposition of $G$ is a set of $k$$H$-decompositions of $G$ such that any two copies of $H$ in distinct $H$-decompositions intersect in at most one edge. When $G=K_v$, we call the $H$-decomposition an $H$-system of order $v$. In this paper, we consider the case $H$ is an $\ell$-cycle and construct a pair of orthogonal $\ell$-cycle systems for all admissible orders when $\ell \in \left\{5,6,7,8,9\right\}$, except when $\ell =v$.