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

The structure of λ -constacyclic codes of length 2 s over the Galois ring GR ( 2 a , m ) is obtained, for any unit λ of the form 4 z − 1 , 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. [ABSTRACT FROM AUTHOR]