Skew Constacyclic Codes over a Non-Chain Ring

Abstract

In this paper, we investigate the algebraic structure of the non-local ring Rq=Fq[v]/⟨v2+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 Rq to be linear complementary dual (LCD). We present some examples of Euclidean LCD codes over Rq and tabulate the parameters of Euclidean LCD codes over finite fields as the Φ-images of these codes over Rq, which are almost maximum distance separable (MDS) and near MDS. Eventually, by making use of Hermitian linear complementary duals of skew constacyclic codes over Rq 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.

Keywords

• non-chain ring
• skew constacyclic codes
• LCD codes
• entanglement-assisted quantum codes