Cyclic Code and Self-Dual Code over $F_2 uF_2 u^2F_2$

Abstract:

      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.