Self-dual and self-orthogonal negacyclic codes of length 2pn over a finite field

Let Fq be a finite field with q elements, q odd. In this paper, we explicitly determine all the self-dual negacyclic codes of length 2pn, n⩾1, over Fq where p is an odd prime coprime to q. We also explicitly determine all the self-orthogonal negacyclic codes of length 2pn, n⩾1, over Fq. As examples we give all the self-dual and self-orthogonal negacyclic codes of length 2⋅3n and length 2⋅11n over F5; all self-orthogonal negacyclic codes of length 2⋅5n and length 2⋅7n over F3.