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

Completely regular codes with covering radius $\rho=1$ must have minimum distance $d\leq 3$. For $d=3$, such codes are perfect and their parameters are well known. In this paper, the cases $d=1$ and $d=2$ 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