A Note on Complete Classification of Repeated-Root σ -Constacyclic Codes of Prime Power Length over F p m [ u ] / ⟨ u 3 ⟩ and their Hamming Distances

This note presents a counterexample to Propositions 7 and 8 in the paper [1], where the authors determine the values of V and W . These values are crucial in determining the Hamming distance and MDS codes in the family of certain constacyclic codes over F p m [ u ] / ⟨ u 3 ⟩ , which implies that the results found in [2] are incorrect. Furthermore, we provide corrections to the aforementioned results.