Optimal Arcs in Hjelmslev Spaces of Large Dimension

The dual construction for arcs in projective Hjelmslev spaces

On maximal arcs in projective Hjelmslev planes over chain rings of even characteristic

In this paper, we prove that maximal (k, 2)-arcs in projective Hjelmslev planes over chain rings R of nilpotency index 2 exist if and only if charR = 4. © 2005 Elsevier Inc. All rights reserved.

2-arcs of maximal size in the affine and the projective Hjelmslev plane over ℤ25

It is shown that the maximal size of a 2-arc in the projective Hjelmslev plane over Z25 is 21, and the (21, 2)-arc is unique up to isomorphism. Furthermore, all maximal (20, 2)-arcs in the affine Hjelmslev plane over Z25 are classified up to isomorphism.

New complete 2 - arcs in the uniform projective Hjelmslev planes over chain rings of order 25

In this paper a 2-arc of size 21 in the projective Hjelmslev plane PHG(2,Z25) and a 2-arc of size 22 in PHG(2,F5[X]/(X)) are given. Both arcs are bigger than the 2-arcs previously known in the respective plane. Furthermore, we will give some information on the geometrical structure of the arcs.

New arcs in projective Hjelmslev planes over Galois rings

It is known that some good linear codes over a finite ring (R-linear codes) arise from interesting point constellations in certain projective geometries. For example, the expurgated Nordstrom-Robinson code, a nonlinear binary [14, 6, 6]-code which has higher minimum distance than any linear binary [14, 6]-code, can be constructed from a maximal 2-arc in the projective Hjelmslev plane over Z4. W...