When isometry and equivalence for skew constacyclic codes coincide

We work in the setting of linear skew constacyclic codes over a commutative base ring $S$. We show that the notions of $(n,σ)$-isometry and $(n,σ)$-equivalence introduced by Ou-azzou et al coincide for most skew $(σ,a)$-constacyclic codes of length $n$, and moreover identify the classes for which th