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

Published 2 Jun 2009 in cs.IT and math.IT | (0906.0550v1)

Abstract: 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.

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