Geodesic
Arcs in projective Hjelmslev planes
Diskretnaya Matematika, Tome 13 (2001) no. 1, pp. 90-109.

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The $(k,n)$-arcs in projective Hjelmslev plane $\mathrm{PHG}(R_R^3)$ over a finite chain ring $R$ are considered. We prove general upper bounds on the cardinality of such arcs and establish the maximum possible size of the projective $(k,n)$-arcs with $n\in\{q^2,\ldots,q^2+q-1\}$. Constructions of projective arcs in the Hjelmslev planes over the chain rings with 4 and 9 elements are also given. 
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I. N. Landjev; T. Khonol'd. Arcs in projective Hjelmslev planes. Diskretnaya Matematika, Tome 13 (2001) no. 1, pp. 90-109. http://geodesic.mathdoc.fr/item/DM_2001_13_1_a5/

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