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A subspace code of size 333 in the setting of a binary q-analog of the Fano plane

Title data

Heinlein, Daniel ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
A subspace code of size 333 in the setting of a binary q-analog of the Fano plane.
In: Advances in Mathematics of Communications. Vol. 13 (August 2019) Issue 3 . - pp. 457-475.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2019029

Project information

Project title:
Project's official titleProject's id
Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche GeometrieNo information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We show that there is a binary subspace code of constant dimension 3 in ambient dimension 7, having minimum distance 4 and cardinality 333,, which improves the previous best known lower bound of 329. Moreover, if a code with these parameters has at least 333 elements, its automorphism group is in 31 conjugacy classes. This is achieved by a more general technique for an exhaustive search in a finite group that does not depend on the enumeration of all subgroups.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Finite groups; finite projective spaces; constant dimension codes; subspace codes; subspace distance; combinatorics; computer search
Subject classification: Mathematics Subject Classification Code: 51E20 (05B07 11T71 94B25)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 17 Apr 2019 07:05
Last Modified: 17 Apr 2019 07:05
URI: https://eref.uni-bayreuth.de/id/eprint/48693