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

We characterize all linear $q$-ary 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 are all classified. 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.

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