  An optimal linear coding solution for index coding problem is established.
Instead of network coding approach by focus on graph theoric and algebraic
methods a linear coding program for solving both unicast and groupcast index
coding problem is presented. The coding is proved to be the optimal solution
from the linear perspective and can be easily utilize for any number of
messages. The importance of this work is lying mostly on the usage of the
presented coding in the groupcast index coding problem.
