English

Completely regular codes in Johnson and Grassmann graphs with small covering radii

Combinatorics 2020-12-15 v1 Information Theory math.IT

Abstract

Let L be a Desarguesian 2-spread in the Grassmann graph Jq(n,2)J_q(n,2). We prove that the collection of the 4-subspaces, which do not contain subspaces from L is a completely regular code in Jq(n,4)J_q(n,4). Similarly, we construct a completely regular code in the Johnson graph J(n,6)J(n,6) from the Steiner quadruple system of the extended Hamming code. We obtain several new completely regular codes covering radius 1 in the Grassmann graph J2(6,3)J_2(6,3) using binary linear programming.

Keywords

Cite

@article{arxiv.2012.06970,
  title  = {Completely regular codes in Johnson and Grassmann graphs with small covering radii},
  author = {I. Yu. Mogilnykh},
  journal= {arXiv preprint arXiv:2012.06970},
  year   = {2020}
}
R2 v1 2026-06-23T20:55:41.182Z