This note gives a counterexample of Theorem 20 in the paper of Blackford (2013) . The counterexample shows that [2, Theorem 20] is incorrect. Furthermore, we provide corrections to the above result.
For any different odd primes ℓ and p, structure of constacyclic codes of length 2ℓmpn over the finite field Fq of characteristic p and their duals is established in terms of their generator polynomials. Among other results, the characterization and enumeration of all linear complementary dual and self-dual constacyclic codes of length 2ℓmpn are obtained.