Cyclic and constacyclic self-dual codes over R_k

In this work, we consider constacyclic and cyclic self-dual codes over the rings R_k. We start with theoretical existence results for constacyclic and cyclic self-dual codes of any length over R_k and then construct cyclic self-dual codes over R₁ = F₂ + uF₂ of even lengths from lifts of binary cyclic self-dual codes. We classify all free cyclic self-dual codes over R₁ of even lengths for which non-trivial such codes exist. In particular we demonstrate that our constructions provide a counter example to a claim made by Batoul et al. in [1] and we explain why their claim fails.