at Google ScholarTitle 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
(2012)
Issue 1
.
- pp. 73-92.
ISSN 1869-1862
DOI: https://doi.org/10.1007/s11425-011-4296-4
Project information
| Project title: |
Project's official title Project's id Konstruktive Methoden in der algebraischen Codierungstheorie für lineare Codes über endlichen Kettenringen 54063226 |
|---|---|
| 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 (Computer Algebra) 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: | 26 Aug 2025 07:31 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/3733 |