This paper explores some theories about the Galois extension of finite chain rings and the definitions of the trace codes and subring subcodes on this Galois extension ring. It is proved that the trace codes of dual codes are the dual of subring subcodes. Moreover, a class of linear codes with parameters [plm-1,m,(pl-1)pl(m-1)] over finite chain rings is also discussed in this paper.%本文给出了有限链环Galois扩张的相关理论，并定义了其Galois扩环上的迹码以及子环子码的概念。证明了有限链环Galois扩环上的对偶码的迹是该扩环上子环子码的对偶码，并给出了有限链环上一类参数为[plm-1，m，（pl-1）pl（m-1）]的线性码。
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