## Title data

Kiermaier, Michael:

**On α-points of q-analogs of the Fano plane.**

*In:* Designs, Codes and Cryptography.
Vol. 90
(2022)
Issue 6
.
- pp. 1335-1345.

ISSN 1573-7586

DOI: https://doi.org/10.1007/s10623-022-01033-3

## Abstract in another language

Arguably, the most important open problem in the theory of q-analogs of designs is the question regarding the existence of a q-analog D of the Fano plane. As of today, it remains undecided for every single prime power order q of the base field. A point P is called an α-point of D if the derived design of D in P is a geometric spread. In 1996, Simon Thomas has shown that there always exists a non-α-point. For the binary case q = 2, Olof Heden and Papa Sissokho have improved this result in 2016 by showing that the non-α-points must form a blocking set with respect to the hyperplanes. In this article, we show that a hyperplane consisting only of α-points implies the existence of a partition of the symplectic generalized quadrangle W(q) into spreads. As a consequence, the statement of Heden and Sissokho is generalized to all primes q and all even values of q.

## Further data

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

Refereed: | Yes |

Keywords: | Subspace design; q-analog; Fano plane; Steiner system; Subspace code |

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: | 10 Sep 2022 21:00 |

Last Modified: | 23 Nov 2022 07:30 |

URI: | https://eref.uni-bayreuth.de/id/eprint/71787 |