Skew Cyclic and Skew Constacyclic Codes over a Mixed Alphabet

In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet R=FqR1R2, where q=pm, p is an odd prime with m odd and R1=Fq+uFq with u2=u, and R2=Fq+uFq+vFq with u2=u,v2=v,uv=vu=0. Such codes consist of the juxtaposition of three codes of the same size over Fq,R1, and R2, respectively. We investigate the generator polynomial for skew cyclic codes over R. Furthermore, we discuss the structural properties of the skew cyclic and skew constacyclic codes over R. We also study their q-ary images under suitable Gray maps.