Cyclic Code and Self-Dual Code over $F_2 uF_2 u^2F_2$
Received:May 11, 2007  Revised:May 07, 2008
Key Words: ring $F_2 uF_2 u^2F_2$   cyclic code   residue code   torsion code   self-dual code.  
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Author NameAffiliation
FENG Qian Qian Department of Mathematics, Xiangfan University, Hubei 441053, China 
ZHOU Wei Gang School of Mathematics and Statistics, Wuhan University, Hubei 430072, China 
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      We give the structures of a cyclic code over ring $$R=F_2 uF_2 u^2F_2=\{0,1,u,u^2,v,v^2,uv,v^3\},$$ where $u^3=0,$ of odd length and its dual code. For the cyclic code, necessary and sufficient conditions for the existence of self-dual code are provided.
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