polycyclic codes over r

In this paper, we  discuss the structure of polycyclic codes over the ring $r=mathbb{f}_q+umathbb{f}_q+vmathbb{f}_q;u^2=alpha u,v^2=v$ and $uv=vu=0$, where $alpha$ is an unit element in $r.$ we introduce annihilator self-dual codes, annihilator self-orthogonal codes and annihilator lcd codes over r. using a gray map, we define a one to one correspondence between $r$ and $mathbb{f}_q$ and  construct quasi polycyclic  codes over the  $mathbb{f}_q$.