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 . We prove that the collection of the 4-subspaces, which do not contain subspaces from L is a completely regular code in . Similarly, we construct a completely regular code in the Johnson graph from the Steiner quadruple system of the extended Hamming code. We obtain several new completely regular codes covering radius 1 in the Grassmann graph 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}
}