We propose the following codoping method with doping both p- and n-type dopants at the same time in order to fabricate the low-resistivity p-type GaN and AIN based upon ab initio electronic structure calculations: (1) GaN: [Si-Ga + 2Mg(Ga)(or Be-Ga), and O-N + 2Mg(Ga)(or Be-Ga)]. (2) AIN: [O-N + 2C(N)]. We compare our predictions of codoping with the recent successful codoping experiments for the low-resistivity p-type GaN and AIN. It is shown that the codoping method enhances the solubility of the dopant., reduces the acceptor energy level, and increases the mobility of the carriers. We predict that the Mn-doped GaN exhibits half-metallic ferromagnetism. in which the majority spin state is metallic and minority spin state is insulating, since the ferromagnetic double exchange interaction overcomes the anti-ferromagnetic super-exchange interaction. It is also shown that the carrier compensation by O donor codoping with the Mn stabilizing the anti-ferromagnetic insulator. We find that Fe-doped GaN is an anti-ferromagnetic insulator because the anti-ferromagnetic super-exchange interaction dominates the magnetism with no contribution from the ferromagnetic double exchange interaction.