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

12/13/2020

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by   I. Yu. Mogilnykh, et al.

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Let 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 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 covering radius 1 in the Grassmann graph J_2(6,3) using binary linear programming.