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| Trace Codes over Galois Extensions of Ring F2+uF2 |
| Wu Bo①②; Zhu Shi-xin② |
| ①Department of Mathematics, Anhui University, Hefei 230039, China;②Department of Applied Mathematics, Hefei University of Technology, Hefei 230009, China |
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Abstract 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.
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Received: 15 May 2006
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2007, Vol. 29 
