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    On linear completely regular codes with covering radius ρ=1\rho=1. Construction and classification

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    Completely regular codes with covering radius ρ=1\rho=1 must have minimum distance d3d\leq 3. For d=3d=3, such codes are perfect and their parameters are well known. In this paper, the cases d=1d=1 and d=2d=2 are studied and completely characterized when the codes are linear. Moreover, it is proven that all these codes are completely transitive.Comment: Submitted to IEEE, Trans. Inf. Theor
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