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.
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 |
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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 |