On q-ary linear completely regular codes with ρ = 2 and antipodal dual

We characterize all q-ary linear completely regular codes with covering radius ρ = 2 when the dual codes are antipodal. These completely regular codes are extensions of linear completely regular codes with covering radius 1, which we also classify. For ρ = 2, we give a list of all such codes known to us. This also gives the characterization of two weight linear antipodal codes. Finally, for a class of completely regular codes with covering radius ρ = 2 and antipodal dual, some interesting properties on self-duality and lifted codes are pointed out. © 2010 AIMS-SDU.