Torsion Codes Of Linear Codes Over Galois Rings And Their Applications

In this paper, the torsion codes and their applications of two classes of constacyclic codes over Galois rings are studied. The details are given as follows:(1) The (ζ~i+pω)-constacyclic codes of arbitrary lengths over Galois rings are studied. Firstly, the structure of a(ζ+pω)-constacyclic code is obtained, which generalizes some results of (1+λp)-constacyclic codes. By using the gotten results, the submodule quotient of (ζi+pω)-constacyclic is obtained and their torsion codes are also obtained.(2) The torsion codes of linear codes over Galois rings are studied. Firstly, the torsion codes are applied to construct MDS codes over Galois rings. And some non-trival MDS codes are obtained. Secondly, the Homogeneous distance and Euclidean distance of (ζi+pω)-constacyclic codes are determined by the torsion codes. We proved that all (1+2ω)-conatcyclic self-dual codes over Z2m are Type I in the meanwhile, and some extreme Type I codes are obtained from such constacyclic codes. Finally, the (1+4ω)-constacyclic codes of length 2k over Galois rings are classified by using the torsion codes. We give the 5-constacyclic self-dual codes of length 8 over Z8 as an application.