On Some Classes of Repeated-root Constacyclic Codes of Length a Power of 2 over Galois Rings

Negacyclic codes of length 2(s) over the Galois ring GR(2(a), m) are ideals of the chain ring GR(2(a),m)[x]/< x(2s)+1 >. This structure is used to provide the Hamming and homogeneous distances of all such negacyclic codes. The technique is then generalized to obtain the structure and Hamming and homogeneous distances of all gamma-constacyclic codes of length 2(s) over GR(2(a), m), where gamma is any unit of the ring GR(2(a), m) that has the form gamma = (4k(0) - 1) 4k(1)xi + ... + 4k(m-1)xi(m-1), for integers k(0), k(1), ..., k(m-1). Among other results, duals of such gamma-constacyclic codes are studied, and necessary and sufficient conditions for the existence of a self-dual gamma-constacyclic code are established.