## Title data

Honold, Thomas ; Kiermaier, Michael:

**The existence of maximal (q², 2)-arcs in projective Hjelmslev planes over chain rings of length 2 and odd prime characteristic.**

*In:* Designs, Codes and Cryptography.
Vol. 68
(2013)
Issue 1–3
.
- pp. 105-126.

ISSN 0925-1022

DOI: https://doi.org/10.1007/s10623-012-9653-y

## Project information

Project financing: |
Deutsche Forschungsgemeinschaft National Natural Science Foundation of China (Grant No. 60872063) Chinese Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200803351027) Deutsche Forschungsgemeinschaft (Grant No. WA 1666/4-1) |
---|

## Abstract in another language

We prove that (q², 2)-arcs exist in the projective Hjelmslev plane PHG(2,R) over a chain ring R of length 2, order |R|=q² and prime characteristic. For odd prime characteristic, our construction solves the maximal arc problem. For characteristic 2, an extension of the above construction yields the lower bound q²+2 on the maximum size of a 2-arc in PHG(2,R). Translating the arcs into codes, we get linear [q³,6,q³-q²-q] codes over F_q for every prime power q>1 and linear [q³+q,6,q³-q²-1] codes over F_q for the special case q=2ʳ. Furthermore, we construct 2-arcs of size (q+1)²/4 in the planes PHG(2,R) over Galois rings R of length 2 and odd characteristic p².

## Further data

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

Refereed: | Yes |

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 07:55 |

Last Modified: | 02 Feb 2022 14:42 |

URI: | https://eref.uni-bayreuth.de/id/eprint/3716 |