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

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

2009-06-02

arxiv.org/abs/0906.0550v1

Computer Science

Information Theory

Submitted to IEEE, Trans. Inf. Theory

Scientific paper

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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