New EAQEC codes from cyclic codes over \({\mathbb {Z}}_{4}+v{\mathbb {Z}}_{4}\)

The dimension of Euclidean hull for a linear code is an important quantity to determine the parameters of an entanglement-assisted quantum error-correcting (EAQEC, for short) code. In this paper, we study the Euclidean hull of a cyclic code over finite non-chain rings \({\mathbb {Z}}_{4}+v{\mathbb {Z}}_{4}\) ${\mathbb{Z}}_4+v{\mathbb{Z}}_4$ , where \(v^2=v\) $v^2=v$ . We provide a method of constructing EAQEC codes by means of our results. This construction is applied to obtain numerous new EAQEC codes, and some of them have better parameters than current EAQEC codes available.