Geodesic
Completely regular codes in Johnson and Grassmann graphs with small covering radii
Ivan Mogilnykh1
1Sobolev Insititute of Mathematics
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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Let ${\cal L}$ be a Desarguesian 2-spread in the Grassmann graph $J_q(n,2)$. We prove that the collection of the $4$-subspaces, which do not contain subspaces from ${\cal L}$ is a completely regular code in $J_q(n,4)$. Similarly, we construct a completely regular code in the Johnson graph $J(n,6)$ from the Steiner quadruple system of the extended Hamming code. We obtain several new completely regular codes with covering radius $1$ in the Grassmann graph $J_2(6,3)$ using binary linear programming.
DOI : 10.37236/10083
Classification : 05B25, 05B30, 94B05, 94B25
Mots-clés : Steiner quadruple system, extended Hamming code

Ivan Mogilnykh  1

1 Sobolev Insititute of Mathematics 
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     author = {Ivan   Mogilnykh},
     title = {Completely regular codes in {Johnson} and {Grassmann} graphs with small covering radii},
     journal = {The electronic journal of combinatorics},
     year = {2022},
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Ivan   Mogilnykh. Completely regular codes in Johnson and Grassmann graphs with small covering radii. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10083

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