English

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

Information Theory 2009-06-03 v1 math.IT

Abstract

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.

Keywords

Cite

@article{arxiv.0906.0550,
  title  = {On linear completely regular codes with covering radius $\rho=1$. Construction and classification},
  author = {J. Borges J. Rifa V. Zinoviev},
  journal= {arXiv preprint arXiv:0906.0550},
  year   = {2009}
}

Comments

Submitted to IEEE, Trans. Inf. Theory

R2 v1 2026-06-21T13:08:54.054Z