## Title data

Etzion, Tuvi ; Kurz, Sascha ; Otal, Kamil ; Özbudak, Ferruh:

**Subspace packings : constructions and bounds.**

*In:* Designs, Codes and Cryptography.
Vol. 88
(September 2020)
.
- pp. 1781-1810.

ISSN 0925-1022

DOI: https://doi.org/10.1007/s10623-020-00732-z

## Abstract in another language

Grassmannian G_q(n,k) is the set of all k-dimensional subspaces of the vector space GF(q)^n. It is well known that codes in the Grassmannian space can be used for error-correction in random network coding. On the other hand, these codes are q-analogs of codes in the Johnson scheme, i.e. constant dimension codes. These codes of the Grassmannian G_q(n,k) also form a family of q-analogs of block designs and they are called subspace designs. The application of subspace codes has motivated extensive work on the q-analogs of block designs. In this paper, we examine one of the last families of q-analogs of block designs which was not considered before. This family called subspace packings is the q-analog of packings. This family of designs was considered recently for network coding solution for a family of multicast networks called the generalized combination networks. A subspace packing t-(n,k,lambda)^m_q is a set S of k-dimensional subspaces from G_q(n,k) such that each t-dimensional subspace of G_q(n,t) is contained in at most lambda elements of S. The goal of this work is to consider the largest size of such subspace packings.

## Further data

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

Refereed: | Yes |

Keywords: | random network coding; subspace codes; packings; designs; q-analogs |

Subject classification: | Mathematics Subject Classification Code: 51E20 (11T71 94B25) |

Institutions of the University: | 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 |

Result of work at the UBT: | Yes |

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

Date Deposited: | 14 Sep 2020 12:28 |

Last Modified: | 14 Sep 2020 12:28 |

URI: | https://eref.uni-bayreuth.de/id/eprint/56989 |