The structure of  λ   -constacyclic codes of length   2 s        2    s          over the Galois ring   GR(2 a ,m)     GR  (    2    a    ,  m  )        is obtained, for any unit  λ    of the form   4z−1     4  z  −  1       ,   z∈GR(2 a ,m)     z  ∈  GR  (    2    a    ,  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.
['Hai Q. Dinh', 'Hongwei Liu', 'Xiusheng Liu', 'Songsak Sriboonchitta']
On structure and distances of some classes of repeated-root constacyclic codes over Galois rings