Optimal binary subspace codes of length 6, constant dimension 3 and minimum distance 4

URN to cite this document: urn:nbn:de:bvb:703-epub-1785-5

Title data

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Optimal binary subspace codes of length 6, constant dimension 3 and minimum distance 4.
Bayreuth , 2014 . - 24 S.

Format: PDF Name: fq11proc.pdf Version: Preprint Available under License German copyright law. This contribution is freely accessible with the consent of the copyright holder on the basis of an (DFG-funded) alliance or national license. The document may be used free of charge for personal use. In addition, the reproduction, editing, distribution and any kind of exploitation require the written consent of the respective rights holder.

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Abstract

It is shown that the maximum size of a binary subspace code of packet length v=6, minimum subspace distance d=4, and constant dimension k=3 is M=77; in Finite Geometry terms, the maximum number of planes in PG(5,2) mutually intersecting in at most a point is 77. Optimal binary (v,M,d;k)=(6,77,4;3) subspace codes are classified into 5 isomorphism types, and a computer-free construction of one isomorphism type is provided. The construction uses both geometry and finite fields theory and generalizes to any q, yielding a new family of q-ary (6,q^6+2q^2+2q+1,4;3) subspace codes.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erschienen in: Kyureghyan, Gohar ; Mullen, Gary L. ; Pott, Alexander (Hrsg.): Topics in Finite Fields. - Providence, Rhode Island : American Mathematical Society , 2015 . - S. 157-176 . - (Contemporary Mathematics ; 632 ) ISBN 978-0-8218-9860-4 DOI: https://doi.org/10.1090/conm/632/12627
Keywords:	subspace code; network coding; partial spread; finite geometry; classification; exhaustive enumeration
DDC Subjects:	000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics
Institutions of the University:	Faculties 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 Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - Univ.-Prof. Dr. Michael Stoll 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 Mathematical Economics > Chair Mathematical Economics - Univ.-Prof. Dr. Jörg Rambau
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-1785-5
Date Deposited:	24 Nov 2014 09:51
Last Modified:	01 Jun 2021 07:44
URI:	https://epub.uni-bayreuth.de/id/eprint/1785

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