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.

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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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