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The maximal size of 6- and 7-arcs in projective Hjelmslev planes over chain rings of order 9

Title data

Honold, Thomas ; Kiermaier, Michael:
The maximal size of 6- and 7-arcs in projective Hjelmslev planes over chain rings of order 9.
In: Science China Mathematics. Vol. 55 (January 2012) Issue 1 . - pp. 73-92.
ISSN 1674-7283
DOI: https://doi.org/10.1007/s11425-011-4296-4

Project information

Project title:
Project's official titleProject's id
Konstruktive Methoden in der algebraischen Codierungstheorie für lineare Codes über endlichen KettenringenWA-1666/4

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We complete the determination of the maximum sizes of (k,n)-arcs, n ≤ 12, in the projective Hjelmslev planes over the two (proper) chain rings ℤ₉=ℤ/9ℤ and S₃=F₃[X]/(X²) of order 9 by resolving the hitherto open cases n=6 and n=7. Part of our proofs rely on decidedly geometric properties of the planes such as Desargues’ Theorem and the existence of certain subplanes.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Hjelmslev geometry; projective Hjelmslev plane; arc; finite chain ring; Galois ring; subplane; affine subplane
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: 20 Nov 2014 13:05
Last Modified: 20 Nov 2014 13:05
URI: https://eref.uni-bayreuth.de/id/eprint/3733