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URN to cite this document: urn:nbn:de:bvb:703-epub-6621-1
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 der Verlagsversion: https://doi.org/10.1007/s10623-022-01033-3
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Abstract
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 |
|---|---|
| Keywords: | Subspace design; q-analog; Fano plane; Steiner system; Subspace code |
| DDC Subjects: | 500 Science > 510 Mathematics |
| 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 |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-6621-1 |
| Date Deposited: | 08 Sep 2022 07:46 |
| Last Modified: | 08 Sep 2022 07:46 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/6621 |
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