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

URN to cite this document: urn:nbn:de:bvb:703-epub-4096-0

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.
Bayreuth , 2019 . - 18 S.

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Name:	fano_paper_333_arxiv.pdf
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Project information

Project title:	Project's official title Project's id Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie No information
Project financing:	Deutsche Forschungsgemeinschaft

Abstract

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 one of 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:	Preprint, postprint
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)
DDC Subjects:	000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics Faculties
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-4096-0
Date Deposited:	17 Jan 2019 09:55
Last Modified:	14 Mar 2019 13:56
URI:	https://epub.uni-bayreuth.de/id/eprint/4096

Available Versions of this Item

A subspace code of size 333 in the setting of a binary q-analog of the Fano plane. (deposited 28 Aug 2017 05:31)
- A subspace code of size 333 in the setting of a binary q-analog of the Fano plane. (deposited 03 May 2018 06:50)
  - A subspace code of size 333 in the setting of a binary q-analog of the Fano plane. (deposited 17 Jan 2019 09:55) [Currently Displayed]

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