Summary: The algebraic structures in term of polynomial generators of all constacyclic codes of length \(2p^s\) over the finite field \(\mathbb F_{p^m}\) are established. Among other results, all self-dual negacyclic codes of length \(2p^s\), where \(p\equiv 1 \pmod 4\) (any \(m\)), or \(p\equiv 3 \pmod 4\) and \(m\) is even, are provided. It is also shown the non-existence of self-dual negacyclic codes of length \(2p^s\), where \(p\equiv 3\pmod 4\), \(m\) is odd, and self-dual cyclic codes of length \(2p^s\), for any odd prime \(p\).