A class of skew constacyclic codes over ℤ4 + uℤ4 with derivation

In this paper, we are interested in the class of [Formula: see text]-constacyclic codes with derivation over the ring [Formula: see text], where [Formula: see text], [Formula: see text] is an automorphism of [Formula: see text] and [Formula: see text] is a [Formula: see text]-derivation (skew derivation). Similar to the case of cyclic codes and their generalizations, we proved a one-to-one correspondence between [Formula: see text]-constacyclic codes and the left [Formula: see text]-submodules of [Formula: see text] As an application, we derived many characterizations of these types of codes. Finally, we provided some examples as applications of the theory developed here.