Negacyclic codes over Galois rings of characteristic 2~a

We investigate negacyclic codes over the Galois ring GR(2 a ,m) of length N = 2 k n, where n is odd and k ⩾ 0. We first determine the structure of u-constacyclic codes of length n over the finite chain ring $GR(2^a ,m)[u]/\langle u^{2^k } + 1\rangle $ . Then using a ring isomorphism we obtain the structure of negacyclic codes over GR(2 a ,m) of length N = 2 k n (n odd) and explore the existence of self-dual negacyclic codes over GR(2 a ,m). A bound for the homogeneous distance of such negacyclic codes is also given.