THE GENERALIZED GRAY IMAGES OF LINEAR CODES OVER F_2+uF_2+vF_2
Gang Tang · Journal of Mathematics · 2012
The generalized Grayφis defined from F2+uF2+vF2 to F4 n 2.The generalized Gray images of linear codes over F2+uF2+vF2 are studied.By using the linearlity of the generality Grayφ,it is proved that the generalized Gray imagesφ(C)of linear codes C over F2+uF2+vF2 are linear codes over F2 and dH(C)=dH(φ(C)).Furthermore,we obtain that φ(C⊥)φ(C)⊥and the generalized Gray imagesφ(C)of cyclic codes C over F2+uF2+vF2 are the 4-quasi-cyclic codes over F2.