## Title data

Kohnert, Axel:

**Sets of type (d₁,d₂) in projective Hjelmslev planes over Galois rings.**

*In:*
Klin, Mikhail (Hrsg.): Algorithmic algebraic combinatorics and Gröbner bases. -
Berlin; Heidelberg
: Springer
,
2009
. - pp. 269-278

ISBN 978-3-642-01959-3

DOI: https://doi.org/10.1007/978-3-642-01960-9_9

## Abstract in another language

In this paper we construct sets of type (d₁, d₂) in the projective Hjelmslev plane. For computational purposes we restrict ourself to planes over Z_(p^s) with p a prime and s > 1, but the method is described over general Galois rings. The existence of sets of type (d₁, d₂) is equivalent to the existence of a solution of a Diophantine system of linear equations. To construct these sets we prescribe automorphisms, which allows to reduce the Diophantine system to a feasible size. At least two of the newly constructed sets are ‘good’ u-arcs. The size of one of them is close to the known upper bound.

## Further data

Item Type: | Article in a book |
---|---|

Refereed: | Yes |

Keywords: | Projective Hjelmslev plane; Two-weight codes; Arcs |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 21 Jan 2015 15:31 |

Last Modified: | 27 Jan 2015 13:09 |

URI: | https://eref.uni-bayreuth.de/id/eprint/5789 |