## Title data

Kiermaier, Michael ; Laue, Reinhard ; Wassermann, Alfred:

**A new series of large sets of subspace designs over the binary field.**

*In:* Designs, Codes and Cryptography.
Vol. 86
(2018)
Issue 2
.
- pp. 251-268.

ISSN 1573-7586

DOI: https://doi.org/10.1007/s10623-017-0349-1

## Project information

Project title: |
Project's official title Project's id Random Network Coding and Designs over GF(q) IC1104 |
---|---|

Project financing: |
COST – European Cooperation in Science and Technology |

## Abstract in another language

In this article, we show the existence of large sets LS_2[3](2,k,v) for infinitely many values of k and v. The exact condition is v ≥ 8 and 0 ≤ k ≤ v such that for the remainders v' and k' of v and k modulo 6 we have 2 ≤ v' ≤ k' ≤ 5.

The proof is constructive and consists of two parts. First, we give a computer construction for an LS_2[3](2,4,8), which is a partition of the set of all 4-dimensional subspaces of an 8-dimensional vector space over the binary field into three disjoint 2-(8, 4, 217)_2 subspace designs. Together with the already known LS_2[3](2,3,8), the application of a recursion method based on a decomposition of the Graßmannian into joins yields a construction for the claimed large sets.

## Further data

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

Refereed: | Yes |

Keywords: | Large set; Subspace design; Recursion; Method of Kramer and Mesner |

Subject classification: | Mathematics Subject Classification Code: 05B05 05B25 51E05 |

Institutions of the University: | 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 and Didactics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 21 Jun 2018 05:24 |

Last Modified: | 23 Nov 2022 08:28 |

URI: | https://eref.uni-bayreuth.de/id/eprint/44593 |