An explicit representation and enumeration for negacyclic codes of length 2^kn over Z₄ + uZ₄

In this paper, we give an explicit representation and enumeration for negacyclic codes of length 2^kn over the local non-principal ideal ring  (u² = 0), where k, n are arbitrary positive integers and n is odd. In particular, we present all distinct negacyclic codes of length 2^k over R precisely. Moreover, we provide an exact mass formula for the number of negacyclic codes of length 2^kn over R and correct several mistakes in some literatures.