Skew Constacyclic Codes over a Non-Chain Ring

In this paper, we investigate the algebraic structure of the non-local ring R[sub.q] =F[sub.q] [v]/〈v[sup.2] +1〉 and identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their duals over this ring. Furthermore, we give a necessary and sufficient condition for the skew constacyclic codes over R[sub.q] to be linear complementary dual (LCD). We present some examples of Euclidean LCD codes over R[sub.q] and tabulate the parameters of Euclidean LCD codes over finite fields as the Φ-images of these codes over R[sub.q] , which are almost maximum distance separable (MDS) and near MDS. Eventually, by making use of Hermitian linear complementary duals of skew constacyclic codes over R[sub.q] and the map Φ, we give a class of entanglement-assisted quantum error correcting codes (EAQECCs) with maximal entanglement and tabulate parameters of some EAQECCs with maximal entanglement over finite fields.