Geodesic
Completely regular designs of strength one
Journal of Algebraic Combinatorics, Tome 3 (1994) no. 2, pp. 177-185.

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Summary: We study a class of highly regular $t$-designs. These are the subsets of vertices of the Johnson graph which are completely regular in the sense of Delsarte [2]. In [9], Meyerowitz classified the completely regular designs having strength zero. In this paper, we determine the completely regular designs having strength one and minimum distance at least two. The approach taken here utilizes the incidence matrix of $( t+1)$-sets versus $k$-sets and is related to the representation theory of distance-regular graphs [1, 5].
Keywords: completely regular subset, equitable partition, Johnson graph, $t$-design 
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     title = {Completely regular designs of strength one},
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Martin, William J. Completely regular designs of strength one. Journal of Algebraic Combinatorics, Tome 3 (1994) no. 2, pp. 177-185. http://geodesic.mathdoc.fr/item/JAC_1994__3_2_a2/