Open Access Kent State (OAKS)

This note gives a counterexample of Theorem 20 in the paper of Blackford (2013) [2]. The counterexample shows that [2, Theorem 20] is incorrect. Furthermore, we provide corrections to the above result.

The algebraic structures in term of polynomial generators of all constacyclic codes of length 2ps over the finite field Fpm are established. Among other results, all self-dual negacyclic codes of length 2ps, where p ≡ 1 (mod 4) (any m), or p ≡ 3 (mod 4) and m is even, are provided. It is also shown the non-existence of self-dual negacyclic codes of length 2ps, where p ≡ 3 (mod 4), m is odd, and self-dual cyclic codes of length 2ps, for any odd prime p.