Skew Constacyclic Codes over a Non-Chain Ring

Abstract

In this paper, we investigate the algebraic structure of the non-local ring R-q = F-q[v]/(v(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-q to be linear complementary dual (LCD). We present some examples of Euclidean LCD codes over R-q and tabulate the parameters of Euclidean LCD codes over finite fields as the F-images of these codes over R-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-q and the map F, 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.