On structure and distances of some classes of repeated-root constacyclic codes over Galois rings

The structure of λ  -constacyclic codes of length 2s2s over the Galois ring GR(2a,m)GR(2a,m) is obtained, for any unit λ   of the form 4z−14z−1, z∈GR(2a,m)z∈GR(2a,m). The duals codes and necessary and sufficient conditions for the existence of a self-dual λ-constacyclic code are provided. Among others, this structure is used to establish the Hamming, homogeneous, and Rosenbloom–Tsfasman distances, and Rosenbloom–Tsfasman weight distribution of all such constacyclic codes.