$2$-arcs of maximal size in the affine and the projective Hjelmslev plane over ${\mathbb{Z}}_{25}$

Abstract

It is shown that the maximal size of a $2$-arc in the projective Hjelmslev plane over ${\mathbb{Z}}_{25}$ is $21$, and the $(21,2)$-arc is unique up to isomorphism. Furthermore, all maximal $(20,2)$-arcs in the affine Hjelmslev plane over ${\mathbb{Z}}_{25}$ are classified up to isomorphism.

20 pages, 3 tables

References in corpus (3)

• New arcs in projective Hjelmslev planes over Galois rings
• Classification of maximal arcs in small projective Hjelmslev geometries
• New complete 2-arcs in the uniform projective Hjelmslev planes over chain rings of order 25