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

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 p.

Official URL: Volltext

Abstract in another language

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, working paper, discussion paper
Additional notes: Erscheint in: Contemporary Mathematics, Vol. 632, 157-172, 2015.
Keywords: subspace code; network coding; partial spread; finite geometry; classification; exhaustive enumeration
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
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 in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 29 Nov 2014 22:00
Last Modified: 14 Mar 2019 15:39
URI: https://eref.uni-bayreuth.de/id/eprint/4475