Trace Codes over Galois Extensions of Ring F2+uF2
环F2+uF2的Galois扩张上的迹码

F2 uF2 is a ring with four elements which shares some good properties of both Z4 and F4.Coding theory over this ring has recently received a great deal of interest among coding theorists.This paper gives the theory of Galois extensions over F2 uF2,and shows that the automorphism groups of these Galois extensions are different from the corresponding groups over Z4.Trace codes and subring subcodes over Galois extensions are defined,and it is proved that the trace codes of dual codes of linear codes are the dual codes of subring subcodes.