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

J. Borges J. Rifa V. Zinoviev

paper

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

arXiv:0906.0550

Abstract

Completely regular codes with covering radius $ρ = 1$ 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.

Submitted to IEEE, Trans. Inf. Theory

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

Abstract

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