Local rings of embedding codepth at most 3 have only trivial   semidualizing complexes
  We prove that a local ring $R$ of embedding codepth at most 3 has at most two semidualizing complexes up to shift-isomorphism, namely, $R$ itself and a dualizing $R$-complex if one exists. 
Saeed Nasseh and Sean Sather-Wagstaff
math.AC