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

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