## Title data

Heinlein, Daniel ; Kurz, Sascha:

**An upper bound for binary subspace codes of length 8, constant dimension 4 and minimum distance 6.**

*In:* Augot, Daniel ; Krouk, Evgeny ; Loidreau, Pierre
(ed.):
The Tenth International Workshop on Coding and Cryptography 2017 : WCC Proceedings. -
Saint-Petersburg
,
2017

## Project information

Project title: |
Project's official title Project's id Integer Linear Programming Models for Subspace Codes and Finite Geometry No information |
---|---|

Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

It is shown that the maximum size A_2(8,6;4) of a binary subspace code of packet length v=8, minimum subspace distance d=4, and constant dimension k=4 is at most 272. In Finite Geometry terms, the maximum number of solids in PG(7,2), mutually intersecting in at most a point, is at most 272. Previously, the best known upper bound A_2(8,6;4)<= 289 was implied by the Johnson bound and the maximum size A_2(7,6;3)=17 of partial plane spreads in PG(6,2). The result was obtained by combining the classification of subspace codes with parameters (7,17,6;3)_2 and (7,34,5;{3,4})_2 with integer linear programming techniques. The classification of (7,33,5;{3,4})_2 subspace codes is obtained as a byproduct.

## Further data

Item Type: | Article in a book |
---|---|

Refereed: | Yes |

Keywords: | subspace codes; network coding; constant dimension codes; subspace distance; integer linear programming; partial spreads |

Subject classification: | Mathematics Subject Classification Code: 51E23 05B40 (11T71 94B25) |

Institutions of the University: | 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 Mathematical Economics Faculties |

Result of work at the UBT: | Yes |

DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |

Date Deposited: | 08 Dec 2017 07:46 |

Last Modified: | 19 Oct 2022 10:27 |

URI: | https://eref.uni-bayreuth.de/id/eprint/40888 |