Group network codes based on exponentiation and multiplication over a subgroup of PGL(2, p)

In this paper, we propose a novel group network coding method over a subgroup H of PGL(2,p) w ith prime p≥5, where the input messages are combined by exponentiation and multiplication under component-wise group operation. Then it is proved that the two-level group network codes in the direct product H" can be constructed by using linear codes over Z_ρ and Z_p-1 as component. Moreover, we present a coding scheme for a concrete network to show our method is better than linear network coding in terms of achieving network coding capacity.