Entanglement-assisted binary quantum codes from skew cyclic codes over F₂ x (F₂ + vF₂)

In the current paper, we study skew cyclic codes over the ring S := F-2 x (F-2 + vF(2)) with v(2) = v. We investigate the structural properties of skew cyclic codes over the ring S. Also, we describe the dual codes of skew cyclic codes with respect to the Euclidean inner product and the Hermitian inner product. Furthermore, we give a necessary and sufficient condition for a skew cyclic code over S to contain its dual. Using these results, we show that binary quantum error-correcting codes as well as entanglement-assisted quantum error-correcting codes can be constructed from skew cyclic codes over S. Finally, we give examples of binary entanglement-assisted quantum error-correcting codes with good parameters from skew cyclic codes over S.