*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.

## 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): | Erscheint in: Contemporary Mathematics, Vol. 632, 157-172, 2015. |

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: | 14 Mar 2019 15:38 |

URI: | https://epub.uni-bayreuth.de/id/eprint/1785 |